Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the

morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred
afternoon classes given he or she is a junior. Round to the nearest thousandth.

freshman
morning 19
afternoon 17
evening 8

sophomore
morning 2
afternoon 3
evening 14

junior
morning 6
afternoon 13
evening 9

senior
morning 16
afternoon 15
evening 7

answer choices

0.571
0.464
0.342
0.158

1 answer

To find the probability that the student preferred afternoon classes given he or she is a junior, we use the formula for conditional probability:

P(afternoon | junior) = P(afternoon and junior) / P(junior)

From the table, we can see that the number of juniors who preferred afternoon classes is 13. The total number of juniors is 6 + 13 + 9 = 28.

So, P(afternoon and junior) = 13/28

The probability of a student being a junior is 28/84, as there are 84 students in total.

So, P(junior) = 28/84

Now we can calculate the probability:

P(afternoon | junior) = (13/28) / (28/84)
= (13/28) * (84/28)
= 1092 / 2352
≈ 0.464

Therefore, the probability that the student preferred afternoon classes given he or she is a junior is approximately 0.464.

The closest answer choice is 0.464.