Q. 11

# 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.

Answer :

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

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