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In a sample of 1000 U.S. adults, 219 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.

User Lenna
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Imagine picking two random people from a group of 1000. Only 219 think celebs are good role models. So, the chance of both agreeing is like picking two "good role model" cards in a row from a deck with fewer of them! Not super likely, about 4.9 %.

Here's how to find the probability that both adults think most celebrities are good role models, without replacement:

1. Proportion of adults who think celebrities are good role models:

219 adults believe celebrities are good role models.

In a sample of 1000, this represents a proportion of 219/1000 = 0.219.

2. Probability of one adult thinking they're good role models:

This is simply the proportion we calculated above: 0.219.

3. Probability of the second adult also thinking they're good role models (without replacement):

Since the first adult is no longer available, there are only 999 adults left.

Out of these, 218 still believe celebrities are good role models (219 total - 1 chosen in the first step).

Therefore, the probability of the second adult also having this opinion is 218/999.

4. Overall probability of both adults having the same opinion:

To get the final probability, we multiply the individual probabilities: 0.219 (first adult) * 218/999 (second adult) ≈ 0.049.

Therefore, the probability that both adults think most celebrities are good role models is approximately 0.049 or 4.9%.

User Kostantinos
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