Question
Arun and Tarun appear for an interview for two vacancies. The probability of Arun's selection is 
and that of Tarun's selection is 
Find the probability that only one of them will be selected.
Solution
Let A denote the event ‘Arun is selected’ and B denote the event ‘Tarun is selected’
Also A and B are independent. A and not B are independent, not A and B are independent.
P (only one of them is 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)
Also A and B are independent. A and not B are independent, not A and B are independent.
P (only one of them is 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)
