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
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of the first adult

The probability that the first adult thinks most celebrities are good role models is $\frac{187}{1100}$.

Step2: Calculate the probability of the second adult

Since the selection is without replacement, for the second adult, there are $187 - 1=186$ adults who think most celebrities are good role models left and $1100- 1 = 1099$ adults in total left. So the probability is $\frac{186}{1099}$.

Step3: Calculate the combined probability

Using the multiplication rule for dependent events $P(A\cap B)=P(A)\times P(B|A)$. Here, $P(A)=\frac{187}{1100}$ and $P(B|A)=\frac{186}{1099}$. Then $P=\frac{187}{1100}\times\frac{186}{1099}=\frac{187\times186}{1100\times1099}=\frac{34782}{1208900}\approx0.029$.

Answer:

$0.029$