Probability formula help

1. Sep 12, 2007

mutzy188

1. The problem statement, all variables and given/known data

P(A) = .7
P(B) = .5
P( [A U B]' ) = .1

Find: P(B|A)

2. Relevant equations

P(B|A) = [P(B intersection A)] / [P(B)]

3. The attempt at a solution

I know the formula:

P(B|A) = [P(B intersection A)] / [P(B)]

but how do I find P(B intersection A)] ?

any help would be greatly appreciated.

Thanks

2. Sep 12, 2007

mattmns

Is there a formula for $P(A \cup B)$ that has $P(A \cap B)$ in it?

3. Sep 12, 2007

mutzy188

Yeah,

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

4. Sep 12, 2007

mattmns

That's the one. Now how can you find P(A U B) with the information you are given?

5. Sep 12, 2007

mutzy188

i dont know. Thats what i got stuck on

6. Sep 12, 2007

mutzy188

I need P(B intersect A)

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

but i dont know how to find P(B U A)

7. Sep 12, 2007

mattmns

If you knew P(X') could you find P(X)?

8. Sep 12, 2007

mutzy188

Yeah,

P(X') = 1 - P(X)

9. Sep 12, 2007

mattmns

And you are given that P([A U B]') = .1, so what is P([A U B])? Now what is P(A intersect B), and finally what is P(B|A)?

edit... You wrote the formula for P(B|A) incorrect. It should be $$P(B|A) = \dfrac{P(A\cap B)}{P(A)}$$.

Last edited: Sep 12, 2007