Question

in a sample of 1200 u.s. adults, 186 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 first - adult

The proportion of adults who think most celebrities are good role models is $p=\frac{186}{1200}= 0.155$.

Step2: Calculate the probability of second - adult

Since we are sampling without replacement, for the second adult, there are 1199 adults left in the sample and 185 adults who think most celebrities are good role models left. So the probability that the second adult thinks most celebrities are good role models given that the first one does is $\frac{185}{1199}$.

Step3: Calculate the joint - probability

The probability that both adults think most celebrities are good role models is the product of the probabilities of each event. So $P=\frac{186}{1200}\times\frac{185}{1199}\approx0.155\times0.154\approx0.024$.

Answer:

$0.024$