# Probability of withdrawal from university

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.

• Your formula is incorrect. $P(O|W) = P(O \cap W)/\mathbf{P(W)}$. Note that you'll have to calculate $P(W)$ from the data given. For this, use the total probability law – stochasticboy321 Nov 5 '15 at 19:57