Question

Clinical studies of 1000 people were analyzed to determine if they have a gene
that predisposes people to have skin cancer. That study revealed that the
probability that a person has the gene predisposed to contract cancer is
0.1.

a) Calculate the probability that 4 or more people have to be analyzed before
two people are detected with the gene.

b) On average, how many people must be analyzed for 2 people to be detected?
with the gene.

Answer 1

a)

probability that 4 or more people have to be analyzed before
two people are detected with the gene is computed here as =P(at most 1 person with gene in first three)

=P(X=0)+P(X=1)

=(4C0)*(0.1)0(0.9)4+(4C1)*(0.1)1(0.9)3

=0.7290+0.2430

=0.972

0.972 is the required

b)

For 2 people to be detected with the gene, average number of people that are to be tested is computed here as:

= 2/p

= 2/0.1 = 20

20 people is the mean number of people required here.

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