Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.1.6

Chapter 4, Problem 4.1.6

Penicillin “Who discovered penicillin: Marcel Bich, William Penn, Jonas Salk, Alexander Fleming, or Louis Pasteur?” If you make a random guess for the answer to that question, what is the probability that your answer is the correct answer of Alexander Fleming?

Verified step by step guidance

Step 1: Identify the total number of possible answers provided in the question. In this case, there are 5 options: Marcel Bich, William Penn, Jonas Salk, Alexander Fleming, and Louis Pasteur.

Step 2: Recognize that the question asks for the probability of randomly guessing the correct answer, which is Alexander Fleming.

Step 3: Recall the formula for probability: \( P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \).

Step 4: Determine the number of favorable outcomes. Since there is only one correct answer (Alexander Fleming), the number of favorable outcomes is 1.

Step 5: Substitute the values into the probability formula: \( P(A) = \frac{1}{5} \). This represents the probability of randomly guessing the correct answer.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance of randomly selecting the correct answer from a set of options. If there are five possible answers, the probability of guessing correctly is 1 out of 5, or 0.2.

Random Guessing

Random guessing refers to making a choice without any prior knowledge or reasoning. In the context of the question, it implies selecting one of the five names without any information about who actually discovered penicillin. This method of selection assumes that each option has an equal chance of being chosen.

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. For this question, the sample space consists of the five names provided: Marcel Bich, William Penn, Jonas Salk, Alexander Fleming, and Louis Pasteur. Understanding the sample space is crucial for calculating the probability of selecting the correct answer.

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Textbook Question

Notation For a polygraph (lie detector) used when a subject is presented with a question, let L= the subject lied and let Y = the polygraph indicated that the subject told a lie. Use your own words to translate the notation P (Y|L) into a verbal statement.

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Textbook Question

In Exercises 17–20, refer to the accompanying table showing results from experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known whether or not the subject lied, so the table indicates when the polygraph (lie detector) test was correct.

False Negative Find the probability of selecting a subject with a negative polygraph result, given that the subject lied. What would be an unfavorable consequence of this error?

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Textbook Question

Exclusive Or The exclusive or means either one or the other event occurs, but not both.

If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

b. Repeat Exercise 11 “Texting or Drinking” using the exclusive or instead of the inclusive or.

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Textbook Question

In Exercises 21-28, find the probability and answer the questions.

Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the expected value of as Mendel claimed?

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Textbook Question

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

SAT Test When making a random guess for an answer to a multiple choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.

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Textbook Question

Women in Movies In a recent year, speaking characters in movies were 68.2% male. What is the probability of randomly selecting a character with a speaking part and getting a female? What should be the value of that probability?

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