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 your answer to the nearest thousandth.

Question

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 your answer to the nearest thousandth.
Freshman Sophomore Junior Senior
Morning: 19 2 6 16
Afternoon: 17 3 13 15
Evening: 8 14 9 7

Bot · Answer

The total number of juniors is 28 (6+13+9). The number of juniors who preferred afternoon classes is 13. Therefore, the probability that a junior preferred afternoon classes is:

$$P(\text{Afternoon} \mid \text{Junior}) = \frac{13}{28} \approx \boxed{0.464}$$