Question

in a sample of 800 u.s. adults, 202 think that most celebrities are good role models. two u.s. adults are selected f 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 0.064(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 0.559(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 is 0.441(round to three decimal places as needed.)

Explanation:

Step1: Calculate the probability of the complement event

The probability that neither adult thinks most celebrities are good role models is given as \(P(\text{neither}) = 0.559\).

Step2: Use the formula for the probability of the complement

The probability that at least one of the two adults thinks most celebrities are good role models is \(P(\text{at least one})=1 - P(\text{neither})\).
Substitute \(P(\text{neither}) = 0.559\) into the formula:
\(P(\text{at least one})=1 - 0.559\)

Step3: Calculate the result

\(1-0.559 = 0.441\)

Answer:

\(0.441\)