In-Class Exercise: Geometric and

Negative Binomial Distributions3-74. 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.

a) What is the probability that 4 or more people will

have to be tested before 2 with the gene are

detected?

b) How many people are expected to be tested

before 2 with the gene are detected?

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)

Solution

.201.0

2)(

.972.0

1.01.011

21.01.01

1

11

))3()2((1)4(

2120

p

rXE

XPXPXP