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In a clinical study, volunteers are tested for a gene that
Chapter 3, Problem 124E(choose chapter or problem)
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 four or more people need to be tested to detect two with the gene?
(b) What is the expected number of people to test to detect two with the gene?
Questions & Answers
QUESTION:
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 four or more people need to be tested to detect two with the gene?
(b) What is the expected number of people to test to detect two with the gene?
ANSWER:
Step 1 of 2
Let x be the no.of persons selected for testing of gene
The probability of a person carries the gene is 0.1
X is following the negative binomial distribution with r=2 and p=0.1
The pmf of the negative binomial distribution is
a) We have to find the probability of 4 or more people need to be tested to detect 2 with the gene
Now
+
= 1-[0.01 + 0.018]
= 0.972
Hence the probability of 4 or more people need to be tested to detect 2 with the gene is 0.972
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