Each person in a group of students was identified by year and asked when he or she preferred taking glasses: 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 senior. Round to the nearest thousandth.

Question

Each person in a group of students was identified by year and asked when he or she preferred taking glasses: 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 senior. Round to the nearest thousandth.

A)0.464
B)0.184
C)0.395
D)0.116

Answer 1

In order to calculate the probability that the student preferred afternoon classes given he or she is a senior, we need to use the conditional probability formula:

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

In this case, A represents preferring afternoon classes and B represents being a senior.

From the table, we see that the number of seniors who prefer afternoon classes is 2. The total number of senior students is 6. Therefore, P(A and B) = 2/12.

The probability that a student is a senior is given by the total number of seniors divided by the total number of students, which is 6/20 = 3/10.

Now we can calculate the probability that the student preferred afternoon classes given he or she is a senior:

P(A|B) = (2/12) / (3/10) = (2/12) * (10/3) = 20/36 = 5/9 ≈ 0.556

Therefore, the probability that the student preferred afternoon classes given he or she is a senior is 0.556. None of the provided answer choices are correct, but the closest one is A)0.464.