"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)
b. Find the probability that neither probable voter would like entertainers to address social and political issues."

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability that neither of the two randomly selected probable voters would like entertainers to address social and political issues. This involves using the Multiplication Rule for independent events.
2. Step 2: Identify the probability of a single voter not wanting entertainers to address social and political issues. From the problem, three out of four voters (or 75%) would like entertainers to address these issues. Therefore, the probability of a voter not wanting entertainers to address these issues is 1 - 0.75 = 0.25.
3. Step 3: Recognize that the two voters are selected independently. This means the probability of both events occurring (neither voter wanting entertainers to address social and political issues) can be calculated by multiplying the probabilities of the individual events.
4. Step 4: Apply the Multiplication Rule. The probability of neither voter wanting entertainers to address social and political issues is given by: ${0.25}^2$. This represents the product of the probabilities for each voter.
5. Step 5: Simplify the expression. The result of ${0.25}^2$ will give the final probability. You can calculate this value to find the numerical result.

Key Concepts

Multiplication Rule

The Multiplication Rule in probability states that the probability of two independent events both occurring is the product of their individual probabilities. This rule is essential when calculating the likelihood of multiple outcomes happening together, especially in scenarios involving random selections.

Independent Events

Independent events are those whose outcomes do not affect each other. In the context of this question, the selection of one probable voter does not influence the selection of another. Understanding independence is crucial for applying the Multiplication Rule correctly.

Complementary Probability

Complementary probability refers to the likelihood of an event not occurring. In this case, if three out of four voters support entertainers addressing issues, the probability that a voter does not support this is one minus that probability. This concept is vital for calculating the probability that neither of the two selected voters supports the idea.