Question

The probability that a student takes a history class and a sociology class is 0.051. The probability that a student takes a history class is 0.32. What is the probability that a student takes a sociology class given that the student is taking a history class?

Answer 1

This is a case of conditional probability. The condition is that the given student, chosen at random, happens to be taking a history class ("given that the student is taking a history class").

The probability that a student takes a history class (alone) is 0.32.

We want P(A|B), where B is the event that the student takes/is taking a history class, and A is the event that the student is taking a sociology glass (alone).

the joint probability that the student is taking BOTH a history and a sociology course at the same time is 0.051.

I'd suggest you look up the formula for "conditional probability." It looks something like

P(A|B) = ----------- , a fraction.