Question
A husband and his wife appears in an interview for two
vacancies in the same clerical post. The probability of husband's selection is 3/5 and the probability of wife's selection is. 1/4, The probability that only one of them is selected is:Solution
Let A= be the event that the husband is selected. and A= be the event that the wife is selected. Then P(A) = 3/5 and P(B) = 1/4 Therefore, not P(A) = 1 - 3/5 = 2/5 not P(B) = 1 - 1/4 = 3/4 ∴  Required probability=P[(A and notB)or(B and notA)] => 3/5 × 3/4 + 1/4 × 2/5 = 9/20 + 2/20 = 11/20
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