Given : let A denote the event ‘Arun is selected’ and let B denote the event ‘ved is selected’.
Therefore , P(A) =
1
4
and P(
¯
B
) =
2
3
⇒
P(B) =
1
3
and P(
¯
A
) =
3
4
Also, A and B are independent .A and not B are independent, not A and B are independent.
To Find: The probability that atleast one of them will get selected.
Now,
P(atleast one of them getting selected)
= P(selecting only Arun ) + P(selecting only ved) + P(selecting both)
= P(A and not B) + P (B and not A) + P (A and B)
= P( A ∩
¯
B
) + P(B ∩
¯
A
) + P(A ∩ B)
=
1
2
Therefore , The probability that atleast one of them will get selected is
1
2
