P(A) = 0.5, P(B) = 0.5, and P(AandB) = 0.05. P(not B ∣ A)= ?

Question

I've attempted this by doing A-B and dividing that answer by A as told, and got it wrong. I did this with a venn diagram and went by a video supplied below the question, and still come up wrong.

I received 9/10 as my answer, it was wrong.

Answer 1

P( not B | A) = P( (not B) and A ) / P(A), using the definition of conditional probability.

We are given P(A), so we need to find P( (not B) and A).

Since B and (not B) partition the sample space, we have that

P(A) = P(A and B) + P(A and (not B) ).

Hence, 0.5 = 0.05 + P(A and (not B) ), so P(A and (not B) ) = 0.45.

Thus,

P( not B | A) = P( (not B) and A ) / P(A) = 0.45/0.5 = 0.90.

Are you sure the provided numbers match those originally given in the problem?

Answer 2

P(not B|A) = 1 - P(B|A) = 1 - P(AB)/P(A) = 1 - .05/.5 = 1 - .1 = .9