Question

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, 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.)

​(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.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

Answer 1

(a)

Out of 800 adulst 199 think that most celebrities are good role models so

P(both adults think most celebrities are good role models) = (199/800) * (198/799) = 0.062

Note the other formula that can be used is:

P(both adults think most celebrities are good role models) = C(199,2) / C(800,2)

(b)

Out of 800 adulst 800 - 199 = 601 do not think that most celebrities are good role models so

P(neither adults think most celebrities are good role models) = (601/800) * (600/799) = 0.564

Note the other formula that can be used is:

P(neither adults think most celebrities are good role models) = C(601,2) / C(800,2)

(c)

This probability can be find by using complement rule. The probability that at least one of the two adults thinks most celebrities are good role models is

P(at least one of the two adults thinks most celebrities are good role) = 1- P(neither adults think most celebrities are good role models) = 1 - 0.564 = 0.436