Description
A and B are events with Pr[A] = 0.25, Pr[B] = 0.32, and Pr[A ∩ B] = 0.06.
Calculate . Pr(A l B')
Explanation & Answer
OK, so we have:
P(A) = 0.25
P(B) = 0.32
P(A and B) = 0.06
So, P(A | B') = P(A given not B).
= ( P(A) - P(A and B) ) / ( 1 - P(B) )
= 0.19 / 0.68
= 0.2794
In other words, we're figuring out how much of A's probability occurs "outside" of B occuring (0.25-0.06 = 0.19); then dividing that by the whole probability of B not occurring (0.68). Drawing a Venn diagram will probably help you to visualise this if it's still a little tough to grasp!