SOLUTION: This is the question: 2 events, A and B, are defined on a sample space S such that P(A|B)= 0.6, P(At least of the events occurs)= 0.8, and P(Exactly one of the events occurs)= 0.6.

Algebra ->  Probability-and-statistics -> SOLUTION: This is the question: 2 events, A and B, are defined on a sample space S such that P(A|B)= 0.6, P(At least of the events occurs)= 0.8, and P(Exactly one of the events occurs)= 0.6.      Log On


   

Question 470503: This is the question: 2 events, A and B, are defined on a sample space S such that P(A|B)= 0.6, P(At least of the events occurs)= 0.8, and P(Exactly one of the events occurs)= 0.6. Find P(A) and P(B).
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
P(A|B) = 0.6,
P(A U B) = 0.8, and
P(A) + P(B) = 0.6.
From P(A U B) = P(A) + P(B) - P(A and B), we get P(A and B) = 0.2.
==> P(A|B) = P(A and B)/P(B), or 0.6 = 0.2/P(B), or P(B) = 0.2/0.6 = 1/3.
Hence, ==> 0.8 = P(A) + 1/3 - 0.2 ==> P(A) = 2/3.