SOLUTION: A and B are independent events. If P(A and B) is 0.4 and P(A or B) is 0.9 find P(A) and P(B) where P(A) is greater than P(B)

Question 1027191: A and B are independent events. If P(A and B) is 0.4 and P(A or B) is 0.9 find P(A) and P(B) where P(A) is greater than P(B)

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let x = P(A) and y = P(B).
Then from the addition law of probability,
0.9 = x+y - 0.4 ==> x+y = 1.3
Also, since A, B are independent events, P(A∩B) = P(A)P(B) = xy = 0.4
==> x(1.3 - x) = 0.4, or
Directly using the quadratic formula, we get the solutions x = 0.8, 0.5.
Since x > y, it follows that P(A) = 0.8 and P(B) = 0.5.
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