Brent K. answered • 06/08/21

Applied Math PhD

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?

Elysia E.

I did exactly this and received 9/10 or .90. It wanted 0.88888888888889 (as given by a key icon beside the answer box in myopenmath). The numbers were copy pasted directly from the question.06/08/21