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Question
A and B are two candidates seeking admission in a college. The probability that A is selected is 0.7 and the probability that exactly one of them is selected is 0.6. Find the probability that B is selected.
Solution
Let p be the probability that B gets selected.
P(Exactly one of A, B is selected) = 0.6 .....(Given)
⇒ P(A is selected, B is not selected; B is selected, A is not selected) = 0.6
⇒ P(A ∩ B′) + P(A′ ∩ B) = 0.6
⇒ P(A) P(B′) + P(A′) P(B) = 0.6
⇒ (0.7)(1 – p) + (0.3)p = 0.6
⇒ p = 0.25
Thus the probability that B gets selected is 0.25.
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