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 .
(round to three decimal places as needed.)

Explanation:

Identify the given values and target

We are given a sample of \(1000\) U.S. adults, where \(195\) think that most celebrities are good role models. Two adults are selected without replacement. We need to find the probability that neither adult thinks most celebrities are good role models, rounded to three decimal places.

Calculate the number of adults who do not think celebrities are good role models

Using the Complementary Events knowledge point

$$ 1000 - 195 = 805 $$

Calculate the probability for the first selection

Using the Dependent Events knowledge point

$$ P(\text{First is "No"}) = \frac{805}{1000} = 0.805 $$

Calculate the probability for the second selection

Using the Dependent Events knowledge point

$$ P(\text{Second is "No"} \mid \text{First is "No"}) = \frac{804}{999} $$

Apply the multiplication rule for dependent events

Using the Multiplication Rule for Probability and Dependent Events knowledge points

$$
LATEXBLOCK0
$$

Rounding to three decimal places gives \(0.648\).

Answer:

(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 <blank>0.648</blank>.
(Round to three decimal places as needed.)