Question

Candidates for a job are interviewed one by one until a qualified candidate is found. Twenty-eight percent of the candidates are qualified. The company has two positions open. They will interview candidates until two qualified candidates are found. Let Y be the number of candidates interviewed up to and including the second qualified candidate. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

Find P(Y = 4).

Answer 1

Let P(Q)= probability of selection of a qualified person.

And let P(N)= probability of non qualified person

Given P(Q)=0.28

Then P(N)= 0.72

Then P(Y=4) can be obtained such that fourth person is surely qualified whose probability is given as 0.28. And Further there be one qualified and two non qualified in the first 3 interview whose probability is given as ³C₁ * (0.28) * (0.72)² = 0.435

Hence required probability is a combination of the above two probabilities. Thus we get

P(Y=4)= 0.28 * 0.435 = 0.122 (Answer).