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.

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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