Question

in a sample of 1100 u.s. adults, 187 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 0.029.
(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 the number of adults who don't think most celebrities are good role models

The total number of adults is \(n = 1100\), and the number of adults who think most celebrities are good role models is \(187\). So the number of adults who don't think so is \(1100 - 187=913\)

Step2: Calculate the probability for the first - selection

The probability that the first - selected adult doesn't think most celebrities are good role models is \(P_1=\frac{913}{1100}\)

Step3: Calculate the probability for the second - selection (without replacement)

After the first non - believer is selected, there are \(1100 - 1 = 1099\) adults left, and \(913-1 = 912\) non - believers left. So the probability that the second - selected adult also doesn't think most celebrities are good role models is \(P_2=\frac{912}{1099}\)

Step4: Calculate the combined probability

Since the two selections are independent (in the sense of conditional probability for without - replacement sampling), the probability that neither adult thinks most celebrities are good role models is \(P = P_1\times P_2=\frac{913}{1100}\times\frac{912}{1099}\)

$$
LATEXBLOCK0
$$

Answer:

\(0.689\)