1. In-Class Exercise: Geometric and Negative Binomial Distributions
3-74. In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1.
What is the probability that 4 or more people will have to be tested before 2 with the gene are detected?
How many people are expected to be tested before 2 with the gene are detected?

2. Solution
Let X be the number of people tested before two are found with gene
X has a negative binomial distribution with r = 2 and p = 0.1.
Part a) asks for P(X ≥ 4)
Part b) asks for E(X)

3. Solution