# Conditional probability

#### Yankel

##### Active member
Hello all

I have a little problem with this short question, would appreciate your help.

Let A and B be two events such that:

P(A|~B) = 1/2 and P(B?AUB) = 2/5

(~B means not B)

Find P(B)

The final answer should be 1/4, I can't get there. I did some work with the conditional probability formula, got P(B)=2/5 * P(AUB) and P(B)=1-2*P(A and ~B). But where do I go from here ?

#### Jameson

Anytime I see the phrase "conditional probability" I always write out the formula: $$\displaystyle P[A|B]=\frac{P[A \cap B]}{P}$$.
In this case we're given: $$\displaystyle P[A|B']=\frac{P[A \cap B']}{P[B']}=\frac{1}{2}$$.