Textbook Question
In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.
25. Event A: Randomly select a red jelly bean from a jar.
Event B: Randomly select a yellow jelly bean from the jar.
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Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.RE.19
In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
19. Tossing a coin four times and getting four heads, and then tossing it a fifth time and getting a head
Verified step by step guidance1
Understand the concept of independence: Two events are independent if the outcome of one event does not affect the outcome of the other. For example, in coin tosses, each toss is independent because the result of one toss does not influence the result of another.
Identify the events in the problem: Event A is tossing a coin four times and getting four heads. Event B is tossing the coin a fifth time and getting a head.
Analyze the relationship between the events: The outcome of the first four tosses (Event A) does not influence the outcome of the fifth toss (Event B). This is because each coin toss is a separate, independent trial with a fixed probability of heads (0.5) or tails (0.5).
Explain the reasoning: Since the probability of getting heads on the fifth toss remains 0.5 regardless of the outcomes of the previous tosses, the events are independent.
Conclude: Based on the analysis, the events are independent because the result of the fifth toss is not affected by the results of the first four tosses.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Independent Events
Independent events are those whose outcomes do not affect each other. In probability, two events A and B are independent if the occurrence of A does not change the likelihood of B occurring, and vice versa. For example, tossing a coin multiple times is independent because the result of one toss does not influence the results of subsequent tosses.
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Probability of Multiple Independent Events
Dependent Events
Dependent events are those where the outcome of one event affects the outcome of another. In probability, if the occurrence of event A changes the probability of event B occurring, then A and B are considered dependent. An example would be drawing cards from a deck without replacement, where the first draw affects the composition of the deck for the second draw.
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Probability of Coin Tosses
The probability of a coin toss is a fundamental concept in statistics, where each toss has two possible outcomes: heads or tails, each with a probability of 0.5. When considering multiple tosses, the outcomes remain independent, meaning the probability of getting heads on the fifth toss remains 0.5, regardless of the results of the previous tosses.
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Related Practice
Textbook Question
In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
8. The probability of randomly selecting five cards of the same suit from a standard deck of 52 playing cards is about 0.002.
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Textbook Question
In Exercises 41-44, perform the indicated calculation.
42. 8P6
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Textbook Question
Telephone Numbers The telephone numbers for a region of Pennsylvania have an area code of 570. The next seven digits represent the local telephone numbers for that region. These cannot begin with a 0 or 1. In Exercises 15 and 16, assume your cousin lives within the given area code.
16. What is the probability of not randomly generating your cousin's telephone number on the first try?
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Textbook Question
In Exercises 41-44, perform the indicated calculation.
44. (5C3)/(10C3)
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Textbook Question
39. You are given that P(A) = 0.15 and P(B) = 0.40. Do you have enough information to find P(A or B)? Explain.
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