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 Sophomore Junior Senior
Morning 19 2 6 16
Afternoon 17 3 13 15
Evening 8 14 9 7
To find the probability that a student preferred afternoon classes given that he or she is a junior, we need to look at the number of juniors who preferred afternoon classes.
For juniors, the number of students who preferred afternoon classes is 13.
Therefore, the probability that a student preferred afternoon classes given he or she is a junior is:
P(afternoon|junior) = Number of juniors who preferred afternoon classes / Number of juniors
P(afternoon|junior) = 13 / (6 + 13 + 9)
P(afternoon|junior) = 13 / 28
P(afternoon|junior) ≈ 0.464
So, the probability that a student preferred afternoon classes given he or she is a junior is approximately 0.464.