Question

"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)
c. Find the probability that at least one of the two probable voters would like entertainers to address social and political issues."

Accepted Answer

Step 1: Understand the problem. We are tasked with finding the probability that at least one of the two probable voters selected at random would like entertainers to address social and political issues. This involves using the complement rule and the multiplication rule. Step 2: Define the probabilities. From the problem, we know that three out of four voters (or 75%) would like entertainers to address social and political issues. Thus, the probability of a voter liking this is P(A) = 0.75, and the probability of a voter not liking this is P(A') = 1 - 0.75 = 0.25. Step 3: Use the complement rule. The probability of 'at least one' liking the issue is the complement of the probability that 'none' of the two voters like the issue. Mathematically, P(at least one) = 1 - P(none). Step 4: Calculate P(none). To find P(none), use the multiplication rule. Since the two voters are selected independently, the probability that both do not like the issue is P(A') * P(A'). Substituting the values, P(none) = 0.25 * 0.25. Step 5: Substitute into the complement formula. Finally, substitute P(none) into the complement formula: P(at least one) = 1 - P(none). This gives the probability that at least one of the two voters would like entertainers to address social and political issues.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Multiplication Rule

Complementary Events

Probability Calculation