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)

Algebra ->  Probability-and-statistics -> 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)       Log On


   

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) About Me  (Show Source):
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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 x%5E2+-+1.3x+%2B0.4+=+0
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.