Question

"A researcher is looking for 10 people to participate to a medical study on diabetes. Suppose a random person on a given list of potential candidates accepts to participate to the study with probability 0.1. What is the probability that the researcher will have to call 25 candidates in order to find his 10 participants?"

Answer 1

0.0000269

Explanation:

Given that a researcher is looking for 10 people to participate to a medical study on diabetes.

Suppose the researcher has to find his 10 participants, out of 25, then he has to get 9 participants in 24 trials, and the last one in 25th trial

Out of 24 trials, 9 participants selecting is binomial with p =0.1 because there are only two outcomes and each trial is independent of the other.

Hence Prob for selecting 9 from 24 = Prob for 9 successes in 24 trials

=P(X=9)

=
`24C9(0.1)^9 (0.9)^(24) \\=0.000269` ...i

the probability that the researcher will have to call 25 candidates in order to find his 10 participants

= i * prob for 25th trial success

=
`0.000269(0.1)\\=0.0000269`