Given : A and B appear for an interview ,then P(A) = and P(B) = P() = and P() =

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) P(B)

=

=

Therefore , The probability that both of them are selected is

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 ) + P(B )

= P(A) P() + P(B) P()

= + )

= +

=

Therefore, the probability that only one of them Is selected is

iii)none is selected

we know that P(none is selected) = P()

= P() P()

=

=

Therefore , the probability that none is selected is

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)

= P( A ) + P(B ) + P( A B)

= P(A) P() + P(B) P() + P(A) P(B)

= + )+

= + +

=

Therefore, the probability that atleast one of them is selected is