# two persons A and B appear in an interview for two vacancies. if the probability of their selection is ¼ and 1/6 respectively. then find the probability that none of them is selected?

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two persons A and B appear in an interview for two vacancies. if the probability of their selection is ¼ and 1/6 respectively. then find the probability that none of them is selected?

## 3 Answers

Q = the event that B is selected.

Given that P(P) = 1/4 and P(Q) = 1/6

We know that P' is the event that A does not get selected and Q' is the event that B does not get selected

Probability that none of them are selected =P(P'∩Q') (∵ Reference : Algebra of Events) =P(P').P(Q') (∵ Here A and B are Independent Events and refer theorem on independent events)

=[ 1 – P(P)][ 1 – P(Q)]

=1−(1/4) x 1−(1/6)

=(3/4)×(5/6)=**5/8**

**HENCE THE ANSWER IS 5/8**

I think this answer is correct,nice question,

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