41. Which value is closest to the probability that the next picture the frame displays will be a picture of a friend?
Answer: C
The probability that the next picture displayed will be a picture of a friend is closest to 0.48.
To determine the probability that the next picture displayed will be a picture of a friend, we first need to calculate the total number of pictures of friends. There are 200 total pictures, with 78 family pictures and 26 pet pictures, 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, which is 96/200 = 0.48.
A) 0.33
This option suggests that the probability of selecting a picture of a friend is 33%. Given that there are 96 pictures of friends out of 200 total pictures, this value does not accurately reflect the proportion of friend pictures and is therefore incorrect.
B) 0.43
A probability of 43% implies that there are 86 pictures of friends (0.43 x 200). However, since there are 96 pictures of friends, this option underestimates the actual number and does not accurately represent the probability.
C) 0.48
This is the correct option as it represents the actual probability of selecting a picture of a friend. With 96 out of 200 pictures being friends, the calculation yields 96/200 = 0.48, accurately reflecting the likelihood of this event.
D) 0.52
A probability of 52% would indicate that there are 104 pictures of friends, which exceeds the actual count of 96. Thus, this option overestimates the number of friend pictures and is incorrect.
E) 0.96
This option suggests an extremely high probability of 96%, which would imply that nearly all pictures are of friends. Given that there are only 96 pictures of friends out of 200, this option is incorrect as it grossly misrepresents the actual figures.
Conclusion
The correct answer is 0.48, as it accurately represents the calculated probability based on the number of pictures of friends relative to the total. All other options either underestimate or overestimate the quantity of friend pictures, making them incorrect in the context of the provided data.