Answer:
0.0000269
Step-by-step 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)
= [tex]24C9(0.1)^9 (0.9)^{24} \\=0.000269[/tex] ...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
= [tex]0.000269(0.1)\\=0.0000269[/tex]
