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.

1 answer

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

P(A|B) = P(A and B) / P(B)

Where:
P(A|B) is the probability of event A given event B
P(A and B) is the probability of both events A and B happening
P(B) is the probability of event B happening

From the table, we see that out of the total number of juniors, 25 preferred afternoon classes.
P(B), the probability that the student is a junior, is 60 out of 100 students.

Now we need to find the probability that a student is a junior and preferred afternoon classes, which is 25 out of 100 students.

Plugging these values into the formula:

P(afternoon|junior) = (25/100) / (60/100) = 25/60 = 0.417 (rounded to the nearest thousandth)

Therefore, the probability that a student preferred afternoon classes given he or she is a junior is 0.417.