Answer to Question #314930 in Statistics and Probability for pal

Question

The human resource management of an insurance company has organized a

recruitment process where all the applicants are MBA graduates. There are 10

applicants and the target for the firm is to recruit 2 MBA graduates. Assuming that the

applicants are independent and each applicant has the same probability of being a

perfect fit, what is the probability that the 5th individual interviewed will be the second

MBA graduate interviewed who is a perfect fit?

Answer 1

At the start probability of 1 student to be perfect is 2/10 and not be perfect 1-2/10=8/10

$(2/10)(8/9)(7/8)(6/7)(1/6)+(8/10)(2/9)(7/8)(6/7)(1/6)+(8/10)(7/9)(2/8)(6/7)(1/6)+(8/10)(7/9)(6/8)(2/7)(1/6)=4\times0.022=0.088$