Consider the population of students attending a university. Suppose that 64% of these students are from Town O, 15% are from Town K, and 21% are from Town T. Of all the students from Town O, 8% eventually withdraw from their program. The withdrawal rates for students from Town K and Town T are 22% and 13%, respectively.
Suppose a student from the university does withdraw from their program. What is the probability that the student is from Town O?
I solved for the probability that a randomly selected student will withdraw, which is 0.1115 and it is correct. I tried P(O|W)= P*(O∩W) / P(O) = 0.08 / 0.1115 = 0.7175 , but this does not match the answer of 0.4592.
Any help is much appreciated!
EDIT: Should be P(O|W)= P*(O∩W) / P(W), sorry for the typo.