Finding P(B intersection A) given P(A), P(B), and P(A∪B)'

[mutzy188]

Homework Statement

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

Find: P(B|A)

The answer is 3/7

Homework Equations

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

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

 

[mattmns]

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

 

[mutzy188]

Yeah,


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

 

[mattmns]

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

 

[mutzy188]

i don't know. Thats what i got stuck on

 

[mutzy188]

I need P(B intersect A)

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


but i don't know how to find P(B U A)

 

[mattmns]

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

 

[mutzy188]

Yeah,

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

 

[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 $$P(B|A) = \dfrac{P(A\cap B)}{P(A)}$$.