Mallory loaded 200 digital pictures into a digital picture frame. 78 are pictures of family members, 26 are pictures of pets, the rest are pictures of friends. The frame displays one 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

Approximately 0.48 represents the probability that the next picture displayed will be a picture of a friend.

To find the probability, we first determine the number of pictures of friends. Mallory loaded 200 pictures, with 78 being family and 26 being pets, leaving 200 - 78 - 26 = 96 pictures of friends. The probability is then calculated as the number of friend pictures divided by the total number of pictures: 96/200 = 0.48.

A (0.33) YOUR ANSWER

This value suggests that only about one-third of the pictures are friends, which is inaccurate given the calculations. With 96 pictures of friends out of 200 total, the probability is much higher than 0.33.

B (0.43) YOUR ANSWER

This option underestimates the number of pictures of friends. A probability of 0.43 would imply that there are approximately 86 pictures of friends, which contradicts the actual count of 96. Thus, this choice is incorrect.

C (0.48) CORRECT

This is the correct choice, accurately representing the probability calculated as 96 friend pictures out of 200 total pictures. The fraction simplifies to 0.48, confirming that nearly half of the pictures are of friends.

D (0.52) YOUR ANSWER

This value indicates that slightly more than half of the pictures are friends, which is incorrect. With only 96 out of 200 pictures being friends, the probability must be lower than 0.52.

E (0.96) YOUR ANSWER

This choice implies that nearly all pictures are of friends, which is far from reality. Since there are only 96 friend pictures, the probability cannot be as high as 0.96, making this an unrealistic option.

Conclusion

The calculation reveals that the probability of the next picture being a friend is approximately 0.48, confirming that about half of the pictures Mallory has loaded into the frame are of friends. The other options misrepresent the distribution of picture types, highlighting the need for precise calculations in probability assessment.