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 
.