Kamal and Vimal appeared for an interview for two vacancies. The probability of Kamal’s selection is 1/3, and that of Vimal’s selection is 3. Find the probability that only one of them will be selected.
Given: let A denote the event ‘kamal is selected’ and let B denote the event ‘vimal is selected’.
Therefore , P(A) = 
and P(B) = 
Also, A and B are independent .A and not B are independent, not A and B are independent.
To Find:The probability that only one of them will be selected.
Now ,
P(only one of them is selected) = P(A and not B or B and not A)
= P(A and not B) + (B and not A)
= P( A 
) + P(B 
)
= P(A) 
P(
) + P(B) 
P(
)
= P(A) 
[1-P(B)]+ P(B) 
[1-P(A)]
= 
[1-
] + 
[1-
]
= 
+ 
= 
Therefore , The probability that only one of them will be selected is 
1