# 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 ->  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

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 Click here to see ALL problems on Probability-and-statistics 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(4012)   (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.