Question

in a sample of 1000 u.s. adults, 213 think that most celebrities are good role models. two u.s. adults are selected 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 (round to three decimal places as needed.)

Explanation:

Step1: Calculate number of adults who don't think so

The number of adults who don't think most celebrities are good role - models is $1000 - 213=787$.

Step2: Calculate the probability of the first - selection

The probability that the first adult selected doesn't think most celebrities are good role - models is $\frac{787}{1000}$.

Step3: Calculate the probability of the second - selection

Since the selection is without replacement, for the second selection, there are 999 adults left and 786 of them don't think most celebrities are good role - models. So the probability that the second adult also doesn't think so is $\frac{786}{999}$.

Step4: Calculate the combined probability

The probability that neither adult thinks most celebrities are good role - models is the product of the probabilities of the two selections, i.e., $P=\frac{787}{1000}\times\frac{786}{999}=\frac{787\times786}{1000\times999}=\frac{620582}{999000}\approx0.621$.

Answer:

$0.621$