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
(round to three decimal places as needed.)

Explanation:

Step1: Calculate first - selection probability

The probability that the first adult thinks most celebrities are good role models is the number of adults who think so divided by the total number of adults in the sample. So, $P_1=\frac{213}{1000}$.

Step2: Calculate second - selection probability

Since the selection is without replacement, for the second selection, there are 999 adults left in the sample and 212 adults who think most celebrities are good role models left. So, $P_2 = \frac{212}{999}$.

Step3: Calculate the joint probability

The probability that both events occur is the product of the probabilities of each event. So, $P = P_1\times P_2=\frac{213}{1000}\times\frac{212}{999}=\frac{213\times212}{1000\times999}=\frac{45156}{999000}\approx0.045$.

Answer:

$0.045$