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.

Imagine 10000 students. .64(10000)= 6400 of them are from town O and .08(6400)= 512 withdraw. .15(10000)= 1500 are from town K and .22(1500)= 330 withdraw. .21(10000)= 2100 are from town T and .13(2100)= 273 a withdraw.

So a total of 512+ 330+ 273= 1115 students withdraw (and 1115 out of 10000 is, as you say 0.0115) and 512 of them, or 512/1115= 0.4592, are from town O.

You used .08 which is the percentage of students from town O without regard that to the number of students from town O- the number of students from the various towns is not the same.