Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima’s selection is 1/7 and that of John’s selection is 1/5. What is the probability that
i. Both of them are selected
ii. Only one of them will be selected
iii. None of them will be selected
Given that,
⇒ P(FS) = P(Fatima’s selection)
⇒ 
⇒ P(FN) = P(Not selecting Fatima)
⇒ 
⇒ 
⇒ P(JS) = P(John’s selection)
⇒ 
⇒ P(JN) = P(Not selecting John)
⇒ 
⇒ 
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 Fatima is selected) + P(only John 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 
.