Given: let A denote the event ‘kamal is selected’ and let B denote the event ‘vimal is selected’.
Therefore , P(A) =
1
3
and P(B) =
1
5
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 ∩
¯
B
) + P(B ∩
¯
A
)
= P(A) x P(
¯
B
) + P(B) x P(
¯
A
)
= P(A) x [1-P(B)]+ P(B) x [1-P(A)]
=
2
5
Therefore , The probability that only one of them will be selected is
2
5
