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

1. 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.
2. 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.
3. 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).
4. 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.
5. 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.

Key Concepts

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.

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.

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.