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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.2.23a
Chapter 3, Problem 3.2.23a

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)
a. Find the probability that both probable voters would like entertainers to address social and political issues.

Verified step by step guidance
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Step 1: Understand the problem. The Multiplication Rule is used to find the probability of two independent events occurring together. Here, we need to calculate the probability that both selected voters would like entertainers to address social and political issues.
Step 2: Determine the probability of a single voter liking entertainers to address social and political issues. From the problem, three out of four voters (or 75%) express this preference. Represent this probability as P(A) = 0.75.
Step 3: Since two voters are selected at random, and the selection is independent, the probability of both voters expressing the same preference can be calculated using the Multiplication Rule: P(A and B) = P(A) × P(B).
Step 4: Substitute the values into the formula. Since P(A) = 0.75 and P(B) = 0.75 (independent events), the formula becomes P(A and B) = 0.75 × 0.75.
Step 5: Perform the multiplication to find the probability. The result will give the probability that both probable voters would like entertainers to address social and political issues.

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Key Concepts

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

Multiplication Rule of Probability

The Multiplication Rule of Probability states that the probability of two independent events both occurring is the product of their individual probabilities. In this context, if the selection of voters is independent, the probability that both selected voters want entertainers to address social issues can be calculated by multiplying the probability of the first voter wanting this by the probability of the second voter wanting it.
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Probability of Multiple Independent Events

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the choice of one voter does not influence the choice of another. Understanding that the selections are independent is crucial for applying the Multiplication Rule correctly, as it allows us to treat the probabilities of each selection separately.
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Probability of Multiple Independent Events

Probability Calculation

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. To find the probability that both selected voters would like entertainers to address social issues, one must first determine the individual probability based on the sample data and then apply the Multiplication Rule to find the combined probability.
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Related Practice
Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

a. The person wears only contacts or only glasses.

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Textbook Question

Shuffle Play You use a shuffle playback feature to randomly play songs in a playlist. The playlist of 56 songs includes 15 instrumental songs.

a. What is the probability that the first three songs to play are instrumental songs? (Assume a song cannot be repeated.)

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Textbook Question

Marijuana Use The percent distribution of the last marijuana use (either medical or nonmedical) for a sample of 13,373 college students is shown in the pie chart. Find the

probability of each event. (Source: American College Health Association)

a. Randomly selecting a student who never used marijuana

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Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. a. 25/25

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Textbook Question

U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census

Bureau)

a. Randomly selecting someone who is under 10 years old

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Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

27. Blood Types The probability that a person of Asian descent in the United States has type O+ blood is 39%. At random, six people of Asian descent in the United States are selected. (Source: American National Red Cross)

a. Find the probability that all six have type O+ blood."

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