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 0.029
(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 0.689
(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
(round to three decimal places as needed.)

Explanation:

Step1: Use complementary probability

The probability that at least one of the two adults thinks most celebrities are good role models is \(P(\text{at least one}) = 1 - P(\text{neither})\).
We know from part (b) that \(P(\text{neither})=0.689\).

Step2: Calculate the required probability

$$P(\text{at least one})=1 - 0.689$$

$$P(\text{at least one}) = 0.311$$

Answer:

\(0.311\)