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Probability - Quant/Math - CAT 2009

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Question 4 the day: July 25, 2003

The question for the day is from the topic of Probability.
If A and B are independent events and P(A) = 0.35 and P(A U B) = 0.75, what is P(B)?

(1) 0.65 (2) 5 / 13
(3) 8 / 13 (4) None of these
Correct Answer - (3)
Solution:

As A and B are independent events, P(A B) = P(A)*P(B)

We know that P(A U B) = P(A) + P(B) - P(A B) = P(A) + P(B) - P(A)*P(B)

=> 0.75 = 0.35 + P(B) - 0.35*P(B)
=> 0.4 = P(B) (1 - 0.35)
=> 0.4 = 0.65 P(B)
=> P(B) =
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