Probability (how to go about doing this qns)?

Question

For events A and B, it is shown that P(A) = 2/3, P(A U B) = 3/4 and P(A and B) = 5/12. Find P(B).

Answer is 0.5

I don't really understand how to do this question. Someone help please? Explanations are greatly needed and appreciated (:

Answer 1

The key is to know the relationship for any events A and B (this will come in handy many times later in the course!)

This is the critical equation relating probabilities for any events A and B:

P(A U B) = P(A) + P(B) - P(A and B)

So, just plug in the numbers and you're set.

3/4 = 2/3 + P(B) - 5/12

P(B) = 3/4 - 2/3 + 5/12 = 6/12 = 0.5