Questions: In a sample of 800 U.S. adults, 197 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.

Solution Steps

• Total number of U.S. adults in the sample: 800
• Number of adults who think most celebrities are good role models: 197

The probability that one adult thinks most celebrities are good role models is: \[ P(A) = \frac{197}{800} \]

Since the selection is without replacement, the probability changes after the first selection.

• Probability that the first adult thinks most celebrities are good role models: \[ P(A_1) = \frac{197}{800} \]
• After selecting one adult who thinks most celebrities are good role models, there are 196 such adults left out of 799 remaining adults.

The probability that the second adult also thinks most celebrities are good role models is: \[ P(A_2|A_1) = \frac{196}{799} \]

The combined probability that both adults think most celebrities are good role models is: \[ P(A_1 \text{ and } A_2) = P(A_1) \times P(A_2|A_1) \] \[ P(A_1 \text{ and } A_2) = \frac{197}{800} \times \frac{196}{799} \]

Final Answer