Step-by-Step Guidance for Introductory Statistics Exam Study

{"type":"doc","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"{\"type\":\"doc\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1a. Find the z-score (standardized score) of a soda with 12.10 ounces. Is this an unusual value?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Z-scores and Normal Distribution\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate a z-score, which measures how many standard deviations a value is from the mean. It also asks you to interpret whether the value is unusual based on its z-score.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Mean (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\mu\"}},{\"type\":\"text\",\"text\":\"): Average value\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Standard deviation (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sigma\"}},{\"type\":\"text\",\"text\":\"): Measure of spread\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Z-score formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{x - \\\\mu}{\\\\sigma}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify the mean (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\mu = 11.98\"}},{\"type\":\"text\",\"text\":\" ounces) and standard deviation (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sigma = 0.03\"}},{\"type\":\"text\",\"text\":\" ounces).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify the value to standardize (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = 12.10\"}},{\"type\":\"text\",\"text\":\" ounces).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Plug these values into the z-score formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{x - \\\\mu}{\\\\sigma}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the numerator (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x - \\\\mu\"}},{\"type\":\"text\",\"text\":\") and denominator (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sigma\"}},{\"type\":\"text\",\"text\":\") separately before dividing.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: z = 4.00 (Unusually high)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{12.10 - 11.98}{0.03} = \\\\frac{0.12}{0.03} = 4.00\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"A z-score of 4 is much higher than typical (usually, z-scores above 2 or below -2 are considered unusual).\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1b. A different can has a z-score of -1.33. How many ounces were in the can of soda?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Z-scores and Reverse Calculation\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the z-score formula to solve for the original value, given the z-score.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Z-score formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{x - \\\\mu}{\\\\sigma}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"To solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x\"}},{\"type\":\"text\",\"text\":\": \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = z \\\\cdot \\\\sigma + \\\\mu\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify the z-score (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = -1.33\"}},{\"type\":\"text\",\"text\":\"), mean (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\mu = 11.98\"}},{\"type\":\"text\",\"text\":\"), and standard deviation (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sigma = 0.03\"}},{\"type\":\"text\",\"text\":\").\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use the rearranged formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = z \\\\cdot \\\\sigma + \\\\mu\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply the z-score by the standard deviation.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add the result to the mean to find the original value.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: 11.94 ounces\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = (-1.33) \\\\cdot 0.03 + 11.98 = -0.0399 + 11.98 = 11.94\"}},{\"type\":\"text\",\"text\":\" ounces\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This can had less than the average volume, as indicated by the negative z-score.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1c. Which is more extreme: a soda can with 12.02 ounces or a tea bottle with 16.80 ounces?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Comparing Z-scores\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate z-scores for two different distributions and compare which value is further from its mean.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Z-score formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{x - \\\\mu}{\\\\sigma}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"\\\"Extreme\\\" means further from zero (the mean).\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For the soda can: Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\mu = 11.98\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sigma = 0.03\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = 12.02\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For the tea bottle: Use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\mu = 16.87\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sigma = 0.04\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"x = 16.80\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the z-score for each using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{x - \\\\mu}{\\\\sigma}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Compare the absolute values of the z-scores to determine which is more extreme.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: Tea bottle is more extreme\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Soda can: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{12.02 - 11.98}{0.03} = 1.33\"}},{\"type\":\"text\",\"text\":\" Tea bottle: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"z = \\\\frac{16.80 - 16.87}{0.04} = -1.75\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The tea bottle's z-score is further from zero, so it is more extreme.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2a. Determine the “5-Number Summary” for this data set: 12, 15, 19, 24, 40, 42, 44, 49, 50, 51\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Descriptive Statistics – 5-Number Summary\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to find the minimum, first quartile (Q1), median, third quartile (Q3), and maximum for a data set.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Minimum: Smallest value\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Q1: First quartile (25th percentile)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Median: Middle value\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Q3: Third quartile (75th percentile)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Maximum: Largest value\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Order the data from smallest to largest (already done).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify the minimum and maximum values.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the median (middle value or average of two middle values).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find Q1 (median of lower half) and Q3 (median of upper half).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write out the five values as the summary.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: Min = 12, Q1 = 19, Med = 41, Q3 = 49, Max = 51\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The 5-number summary gives a quick overview of the spread and center of the data.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2b. What is the percentile of “24” in the data set?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Percentiles\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to find the percentile rank of a value in a data set.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Percentile formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Percentile} = \\\\frac{\\\\text{Number of values below}}{\\\\text{Total number of values}} \\\\times 100\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Count how many values are below 24 in the data set.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Divide by the total number of values (10).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply by 100 to get the percentile.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: 30th percentile\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"There are 3 values below 24, so \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{3}{10} \\\\times 100 = 30\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2c. What number is at the 72nd percentile?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Percentiles and Data Position\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to find the value at a given percentile using the formula for position.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Position formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Position} = \\\\frac{p}{100} \\\\times n\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Round up to the next whole number if not an integer.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the position: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{72}{100} \\\\times 10\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Round up to the next whole number.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the value at that position in the ordered data set.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: 49\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Position is 7.2, so round up to 8th value, which is 49.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2d. Calculate the IQR and determine if there are any outliers\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Interquartile Range and Outlier Detection\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate the IQR and use it to check for outliers.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"IQR: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{IQR} = Q3 - Q1\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Outlier cutoff: Below \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"Q1 - 1.5 \\\\times \\\\text{IQR}\"}},{\"type\":\"text\",\"text\":\" or above \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"Q3 + 1.5 \\\\times \\\\text{IQR}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate IQR using Q1 and Q3 from earlier.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Compute the lower cutoff: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"Q1 - 1.5 \\\\times \\\\text{IQR}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Compute the upper cutoff: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"Q3 + 1.5 \\\\times \\\\text{IQR}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Check if any values in the data set fall outside these cutoffs.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: IQR = 30, No outliers\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"IQR = 49 - 19 = 30. Cutoffs: below -26 or above 94. All values are within this range.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2e. Draw the boxplot. Identify any outliers.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Boxplots and Outlier Identification\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to construct a boxplot and visually identify outliers.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Boxplot: Visual summary of the 5-number summary\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Whiskers: Extend to min and max unless outliers are present\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Draw a box from Q1 to Q3, with a line at the median.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Extend whiskers to min and max values.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Mark any outliers (none in this case).\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: Boxplot from 12 to 51, no outliers\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Box between 19 and 49, median at 41, whiskers to 12 and 51. No outliers.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q3. How many possible simple events of response sets are possible for a quiz with T/F, A/B/C/D, and Yes/No/Maybe?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Counting Principle and Sample Space\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the multiplication rule to count the number of possible outcomes.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Counting Principle: Multiply the number of choices for each event\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Sample space: All possible outcomes\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Count the number of choices for each question: T/F (2), A/B/C/D (4), Yes/No/Maybe (3).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Multiply these numbers together to get the total number of possible response sets.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: 24 simple events\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"2 x 4 x 3 = 24 possible response sets.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q4a. Name two events that are disjoint in a standard deck of 52 cards.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Probability – Disjoint (Mutually Exclusive) Events\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of disjoint events, which cannot occur at the same time.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Disjoint events: No overlap, cannot happen together\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Think of two events that cannot both be true for a single card (e.g., Ace and Jack).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write down two such events.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: Ace and Jack\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"A card cannot be both an Ace and a Jack at the same time.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q4b. Name two events that are not disjoint in a standard deck of 52 cards.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Probability – Non-Disjoint Events\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of events that can overlap.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Non-disjoint events: Can occur together\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Think of two events that can both be true for a single card (e.g., Ace and Spade).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write down two such events.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: Ace and Spade\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"A card can be both an Ace and a Spade (Ace of Spades).\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q4c. Find the probability that a randomly selected card is:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"i) A King?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"ii) Not a King?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iii) A Heart suit?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iv) A King and a Heart?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"v) 10 or a 7?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vi) 10 and a 7?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vii) Black?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"viii) Black and a King?\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"ix) Black or a King?\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Basic Probability with Cards\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate probabilities for various events in a deck of cards.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Probability: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(E) = \\\\frac{\\\\text{Number of favorable outcomes}}{\\\\text{Total outcomes}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use addition and multiplication rules as needed.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For each event, count the number of favorable cards (e.g., 4 Kings, 13 Hearts, etc.).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Divide by 52 to get the probability.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \\\"or\\\" events, use \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(A \\\\text{ or } B) = P(A) + P(B) - P(A \\\\text{ and } B)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \\\"and\\\" events, count cards that satisfy both conditions.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the fractions for each event, but stop before calculating the final decimal.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"i) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{4}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"ii) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{48}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iii) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{13}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iv) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{1}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"v) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{8}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vi) $0"},{"type":"inlineMath","attrs":{"latex":"\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vii) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{26}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"viii) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{2}{52}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"ix) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{28}{52}\"}}]}]}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Each probability is calculated based on the number of cards that fit the description.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q5a. What is the sample space of configurations of heads and tails for four coin tosses? How many are possible?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Sample Space and Counting Principle\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to list all possible outcomes and count them.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Sample space: All possible outcomes\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Each toss: 2 outcomes (H or T)\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Each toss has 2 outcomes, so for 4 tosses: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2^4\"}},{\"type\":\"text\",\"text\":\" possible outcomes.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"List all possible combinations (e.g., HHHH, HHHT, etc.).\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: 16 possibilities\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"There are \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2^4 = 16\"}},{\"type\":\"text\",\"text\":\" possible outcomes, including HHHH, HHHT, ..., TTTT.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q5b. What is the probability that the flips will result in exactly 2 heads and 2 tails?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Binomial Probability\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use combinations to find the probability of a specific outcome.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Number of ways: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\binom{4}{2}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Probability: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P = \\\\frac{\\\\text{Number of ways}}{\\\\text{Total outcomes}}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the number of ways to get 2 heads in 4 tosses: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\binom{4}{2}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Total outcomes: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2^4 = 16\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the probability fraction: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\binom{4}{2}}{16}\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{6}{16}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"There are 6 ways to get 2 heads and 2 tails out of 16 possible outcomes.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q5c. What is the probability of at least 1 head out of 4 coin tosses?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Probability – Complement Rule\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the complement rule to find the probability of \\\"at least one\\\" event.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Complement rule: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(\\\\text{at least one}) = 1 - P(\\\\text{none})\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Probability of all tails: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{1}{16}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the probability of getting no heads (all tails).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract this from 1 to get the probability of at least one head.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{15}{16}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Only one outcome is all tails; the rest have at least one head.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q6a. Fill in the missing numbers in the table from a survey of 500 people.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Contingency Tables\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to fill in missing values in a two-way table using totals.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Row and column totals\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract known values from totals to find missing values\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use the totals for each row and column to find missing values.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract known values from the total to find each missing cell.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: Table filled\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null}},{\"type\":\"table\",\"content\":[{\"type\":\"tableRow\",\"content\":[{\"type\":\"tableHeader\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null}}]},{\"type\":\"tableHeader\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"A\"}]}]},{\"type\":\"tableHeader\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"B\"}]}]},{\"type\":\"tableHeader\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"C\"}]}]},{\"type\":\"tableHeader\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Total\"}]}]}]},{\"type\":\"tableRow\",\"content\":[{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"D\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"60\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"100\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"90\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"250\"}]}]}]},{\"type\":\"tableRow\",\"content\":[{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"E\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"30\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"75\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"20\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"125\"}]}]}]},{\"type\":\"tableRow\",\"content\":[{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"F\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"10\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"25\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"90\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"125\"}]}]}]},{\"type\":\"tableRow\",\"content\":[{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Total\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"100\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"200\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"200\"}]}]},{\"type\":\"tableCell\",\"attrs\":{\"colspan\":1,\"rowspan\":1,\"colwidth\":null,\"align\":null},\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"500\"}]}]}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q6b. If a single person is selected at random from the table, find the following probabilities:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"i) P(A)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"ii) P(A or B)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iii) P(A and B)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iv) P(A and E)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"v) P(A or E)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vi) P(A | E)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vii) P(E | A)\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Probability from Contingency Tables\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate various probabilities from a two-way table, including joint, marginal, and conditional probabilities.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formula:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Marginal probability: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(A) = \\\\frac{\\\\text{Total in A}}{\\\\text{Grand total}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Joint probability: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(A \\\\text{ and } B) = \\\\frac{\\\\text{Number in both}}{\\\\text{Grand total}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Conditional probability: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(A | E) = \\\\frac{\\\\text{Number in both}}{\\\\text{Total in E}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Addition rule: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"P(A \\\\text{ or } B) = P(A) + P(B) - P(A \\\\text{ and } B)\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For each probability, identify the relevant counts from the table.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Set up the fraction for each probability (e.g., \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{100}{500}\"}},{\"type\":\"text\",\"text\":\" for P(A)).\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For conditional probabilities, use the \\\"given\\\" group as the denominator.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \\\"or\\\" probabilities, use the addition rule.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"i) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{100}{500}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"ii) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{300}{500}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iii) $0"}},{"type":"text","text":"\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"iv) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{30}{500}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"v) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{195}{500}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vi) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{30}{125}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"vii) \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{30}{100}\"}}]}]}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Each probability is based on the counts in the table.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q7a. What is the probability that both marbles picked are green (without replacement)?\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Probability – Dependent Events\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to calculate probabilities when events are dependent (without replacement).\"}]},{\"type\":\"