Question
Fatima and John appear in an interview for two vacancies in the same post. The probability of Fatima's selection is 
that of John's selection is 
What is the probability that only one of them is selected?
Solution
Let A : Fatima is selected
B : John is selected
Clearly ‘A’ and ‘B’ are independent.
P(only one of them will be selected)
= P('A and not B' or 'B and not A')
= P(A and not B) + P(B and not A)
= P(A) P(not B) + P(B) P(not A)
= P(A) [1 - P(B)] + P(B) [1 - P(A)]
