Q. 11. The probability of a college student being male is 1/3 and that of being female is 2/3. The probability that a male student completes the course is 3/4 and that a female student does it is 1/2. A student is selected at random and is found to have completed the course. What is the probability that the student is a male? (Dec. 2001)

Solution. This problem is based on Bayes theorem.
Let A = an event that the student completes the course
B₁ = an event that the student selected is male
B₂ = an event that the student selected is female

Therefore, P(B₁) = 1/3, P(B₂) = 2/3
P(A | B₁) = 3/4, P(A | B₂) = 1/2

or P(B₁ | A) = 0.428
Thus, the probability that the student being male is 0.428.