Q14 of 249 Page 32

A husband and wife appear in an interview for two vacancies for the same post. The probability of husband’s selection is 1/7 and that of wife’s selection is 1/5. What is the probability that

i. Both of them will be selected


ii. Only one them will be selected


iii. None of them will be selected

Given that,


⇒ P(HS) = P(Husband’s selection)


⇒


⇒ P(HN) = P(Not selecting Husband)


⇒


⇒


⇒ P(WS) = P(wife’s selection)


⇒


⇒ P(WN) = P(Not selecting Wife)


⇒


⇒


We need to find:


i. Both of them will be selected


ii. Only one of them will be selected


iii. None of them will be selected


⇒ P(Sboth) = P(Both of them are selected)


Since selection of each person is an independent event their probabilities multiply each other


⇒


⇒


⇒


⇒ P(Sone) = P(Only one of them is selected)


⇒ P(Sone) = P(only Husband is selected) + P(only Wife is selected)


Since selection of each person is an independent event their probabilities multiply each other


⇒


⇒


⇒


⇒ P(Snone) = P(None of them are selected)


Since selection of each person is an independent event their probabilities multiply each other


⇒


⇒


⇒


∴ The required probabilities are .


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