Q. 12

Arun and Ved appeared for an interview for two vacancies. The probability of Arun’s selection is 1/4, and that of Ved’s rejection is 2/3. Find the probability that at least one of them will be selected.

Answer :

Given : let A denote the event ‘Arun is selected’ and let B denote the event ‘ved is selected’.


Therefore , P(A) = and P() = P(B) = and P() =


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


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


= + )+


= + +


=


Therefore , The probability that atleast one of them will get selected is


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