Question

in a sample of 1000 u.s. adults, 195 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 0.038.
(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 0.648.
(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:

Identify the given values and target

Using the At Least One Probability knowledge point
We are given:

• Total sample size \(N = 1000\)
• Number of adults who think most celebrities are good role models \(A = 195\)
• Number of adults who do not think so \(B = 1000 - 195 = 805\)
• Two adults are selected without replacement.
• We need to find the probability that at least one of the two adults thinks most celebrities are good role models.

Apply the complement rule

Using the At Least One Probability knowledge point

$$ P(\text{at least one}) = 1 - P(\text{neither}) $$

Calculate the final probability

Using the At Least One Probability knowledge point

$$
LATEXBLOCK0
$$

Answer:

(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 <blank>0.352</blank>
(Round to three decimal places as needed.)