Question

in a sample of 1000 u.s. adults, 213 think that most celebrities are good role models. two - adults are selected at random from this sample without replacement. complete parts (a) through (c). (a) find the probability that both adults think most celebrities are good role models. the probability that both adults think most celebrities are good role models is 0.045 (round to three decimal places as needed.) (b) find the probability that neither adult thinks most celebrities are good role models. the probability that neither adult thinks most celebrities are good role models is 0.619 (round to three decimal places as needed.) (c) find the probability that at least one of the two adults thinks most celebrities are good role models. the probability that at least one of the two adults thinks most celebrities are good role models is (round to three decimal places as needed.)

Explanation:

Step1: Calculate complementary - probability relationship

The probability that at least one of the two adults thinks most celebrities are good role models is the complement of the event that neither adult thinks most celebrities are good role models. Let \(P(\text{neither})\) be the probability that neither adult thinks most celebrities are good role models and \(P(\text{at least one})\) be the probability that at least one of the two adults thinks most celebrities are good role models. Then \(P(\text{at least one})=1 - P(\text{neither})\).

Step2: Substitute the known value

We know from part (b) that \(P(\text{neither}) = 0.619\). So \(P(\text{at least one})=1 - 0.619\).

Step3: Calculate the result

\(P(\text{at least one})=0.381\)

Answer:

\(0.381\)