conditional probability

Question

How do I figure out how to do P(A' l B') given P(A and B), P( A' or B'), and P(B)?

Answer 1

This problem can't be solved with the information given as, though we can find P(B'), we can't find P(A'B')

Consider the following three examples where P(B) = .5, P(A' or B') = .75, and P(A and B) = .25 in all 3.

Example 1. P(AB) = .25 P(AB') = .25 P(A'B) = .25 P(A'B') = .25

P(A'B'|B') = .25/.5 = .5

Example 2. P(AB) = .25 P(AB') = .5 P(A'B) = .25 P(A'B') = 0

P(A'B'|B') = 0/.5 = 0

Example 3. P(AB) = .25 P(AB') = 0 P(A'B) = .25 P(A'B') = .5

P(A'B'|B') = .5/.5 = 1

We met the same given in all three examples, with three different results.