SOLUTION: Suppose E,F are events in a sample space S. Suppose Pr (E|F)=3/4 and Pr (F|E)= 1/2 and Pr (EUF)=2/3. Find Pr (E) and Pr (F)

Question 1024793: Suppose E,F are events in a sample space S. Suppose Pr (E|F)=3/4 and Pr (F|E)= 1/2 and Pr (EUF)=2/3. Find Pr (E) and Pr (F)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
P(E|F) = P(E∩F)/P(F) ==>P(F) = (4/3)P(E ∩ F)
P(F|E) = P(E∩F)/P(E) ==>P(E) = 2P(E ∩ F)
==> P(E U F) = P(E) + P(F) - P(E ∩F) = 2P(E ∩ F) + (4/3)P(E ∩ F) - P(E ∩F) = (7/3)P(E ∩F)
==> 2/3 = (7/3)P(E ∩F)
==> 2 = 7P(E ∩F), or
P(E ∩F) = 2/7.
==> P(E) = 2P(E ∩ F) = 4/7, and
==> P(F) = (4/3)P(E ∩ F) = 8/21.
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