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 senior. Round to the nearest thousandth.
Responses
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A0.395
B0.116
C0.184
D0.464
To find the probability that the student preferred afternoon classes given he or she is a senior, 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 A given B, P(A and B) is the probability of both A and B happening, and P(B) is the probability of B happening.
From the table:
- Number of seniors who preferred afternoon classes = 26
- Total number of seniors = 100
Therefore, P(A and B) = 26/200 = 0.13
- Number of students who preferred afternoon classes = 91
- Total number of students = 250
Therefore, P(B) = 91/250 = 0.364
Now, we can calculate the conditional probability:
P(A|B) = P(A and B) / P(B)
P(afternoon classes | senior) = 0.13 / 0.364
P(afternoon classes | senior) ≈ 0.357
So, the probability that the student preferred afternoon classes given he or she is a senior is 0.357, which rounds to 0.357 to the nearest thousandth.
Therefore, the answer is:
B) 0.357