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 .
(round to three decimal places as needed.)

Explanation:

Identify the given values

Using the Dependent Events knowledge point

• Total sample size \(N = 1000\)
• Number of adults who think celebrities are good role models \(A = 195\)
• Two adults are selected without replacement.

Calculate the probability of the first selection

Using the Dependent Events knowledge point

$$ P(E_1) = \frac{195}{1000} = 0.195 $$

Calculate the probability of the second selection

Using the Dependent Events knowledge point

$$ P(E_2 \mid E_1) = \frac{195 - 1}{1000 - 1} = \frac{194}{999} $$

Apply the multiplication rule

Using the Multiplication Rule for Probability knowledge point

$$ P(E_1 \text{ and } E_2) = P(E_1) \times P(E_2 \mid E_1) = \frac{195}{1000} \times \frac{194}{999} = \frac{37830}{999000} \approx 0.03786787 $$

Round to three decimal places

Using the Multiplication Rule for Probability knowledge point

$$ P(E_1 \text{ and } E_2) \approx 0.038 $$

Answer:

The probability that both adults think most celebrities are good role models is <blank>0.038</blank>.