In a clinical study volunteers are tested for a gene that ha

In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The

probability that the person carries a gene is 0.1

(a) What is the probability that 4 or more people will have to be tested in order to detect one person with

the gene?

(b) How many people are expected to be tested in order to detect one person with the gene?

(c) How many people are expected to be tested before 2 with a gene are detected?

I want full explain the way you do please mention what type of the distribution it is

Solution

If X is the number of steps before the 1st success, then X has geometric distribution with p = 0 . 1 (success = gene detection). To compute
a)
P(X>=4) = (1-p)^3 = (1-0.1)^3 = 0.729

b)
E(X) = U = 1/p = 1/0.1 = 10

c)
E(X) = 10*2 = 20