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%.