Difficulty: Easy

Average Score: 100%

Mallory loaded 200 digital pictures into a digital picture frame. Of these pictures, 78 are pictures of family members, 26 are pictures of pets, and the rest are pictures of friends. The frame displays a randomly selected picture every 10 seconds.

Which value is closest to the probability that the next picture the frame displays will be a picture of a friend?

Rationale

0.48 is the closest value to the probability that the next picture the frame displays will be a picture of a friend.

The probability of the next picture being of a friend is calculated based on the ratio of friend pictures to the total number of pictures displayed. In this case, 0.48 represents an approximate likelihood based on the distribution of images in the frame.

A (0.33) YOUR ANSWER

This value indicates a lower probability than what is suggested by the distribution of pictures. A probability of 0.33 would imply that only one-third of the pictures are of friends, which does not accurately reflect the given data.

B (0.43) YOUR ANSWER

While this option is closer than 0.33, it still underestimates the probability of the next picture being a friend. A probability of 0.43 suggests a less than even chance of displaying a friend, which is not consistent with the available information.

D (0.52) YOUR ANSWER

This value exceeds the actual probability of 0.48. It suggests that slightly more than half of the pictures are of friends, which would be an overestimation of the likelihood based on the provided context.

E (0.96) YOUR ANSWER

This option represents an extremely high probability, implying that almost all pictures in the frame are of friends. Such a value drastically misrepresents the actual distribution and is not a realistic assessment of the situation.

Conclusion

The probability that the next picture displayed in the frame will be of a friend is best represented by the value of 0.48. This reflects the correct ratio of friend pictures to total pictures, while the other options either underestimate or overestimate the likelihood, failing to accurately represent the scenario. Understanding these probabilities is crucial in making informed predictions about future outcomes based on observed distributions.