To find the probability that the student was male given they got a 'C', we need to use Bayes' theorem. Bayes' theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where P(A|B) is the probability of event A given event B, P(B|A) is the probability of event B given event A, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In this case, event A is "the student is male" and event B is "the student got a 'C'". We are given the following information:
- P(A) = 31/64 (the prior probability of a student being male)
- P(B|A) = 4/31 (the probability of getting a 'C' given the student is male)
- P(B) = 20/64 (the prior probability of getting a 'C')
Using Bayes' theorem, we can calculate P(A|B) as:
P(A|B) = P(B|A) * P(A) / P(B)
P(A|C) = (4/31) * (31/64) / (20/64)
P(A|C) = 4/20
P(A|C) = 0.2
Therefore, the probability that the student was male given they got a 'C' is 0.2 or 20%.