Given : A and B appear for an interview ,then P(A) =
1
6
and P(B) =
1
4
⇒
P(
¯
A
) =
5
6
and P(
¯
B
) =
3
4
Also, A and B are independent .A and not B are independent, not A and B are independent.
To Find:
(i) The probability that both of them are selected.
We know that, P( both of them are selected) = P(A ∩ B) = P(A) x P(B)
=
1
6
×
1
4
=
1
24
Therefore , The probability that both of them are selected is
1
24
(ii) 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
)
=
1
3
Therefore, the probability that only one of them Is selected is
1
3
(iii) none is selected
we know that P(none is selected) = P(
¯
A
∩
¯
B
)
= P(
¯
A
) x P(
¯
B
)
=
5
6
×
3
4
=
5
8
Therefore , the probability that none is selected is
5
8
(iv) atleast one of them is selected
Now, P(atleast one of them is selected)
= P(selecting only A ) + P(selecting only B) + P(selecting both)
= P(A and not B) + P (B and not A) + P (A and B)
=
3
8
Therefore, the probability that atleast one of them is selected is
3
8
