39. 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?
Answer: C
The probability that the next picture displayed will be a picture of a friend is approximately 0.48.
To determine the probability that the next picture the frame displays 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 friends' pictures divided by the total number of pictures, which gives us 96/200 = 0.48.
A) 0.33
This option suggests a probability of 0.33, which would indicate that there are approximately 66 pictures of friends. However, this contradicts the earlier calculation that shows 96 pictures of friends. Thus, this option is incorrect.
B) 0.43
A probability of 0.43 implies that there are around 86 pictures of friends. Since we calculated that there are actually 96 pictures of friends, this option does not accurately reflect the data and is therefore incorrect.
C) 0.48
This value correctly represents the probability of selecting a picture of a friend. As calculated, there are 96 pictures of friends out of a total of 200 pictures, yielding a probability of 96/200 = 0.48. Thus, this option is the correct answer.
D) 0.52
A probability of 0.52 would suggest there are about 104 pictures of friends, which exceeds the actual count of 96. This discrepancy indicates that this option does not align with the provided data and is incorrect.
E) 0.96
This option implies an overwhelming majority of the pictures are friends' pictures, approximately 192 out of 200. However, since we only calculated 96 pictures of friends, this option is significantly overstated and therefore incorrect.
Conclusion
The correct answer is 0.48, as it accurately reflects the calculated probability based on the given data. All other options fail to match the actual count of friends' pictures, either underestimating or overestimating their presence in the total picture set. Therefore, C is the only viable choice based on the information provided.