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5. 11 points In a clinical study, volunteers are tested for a gene that has been found 5 to increase the risk for a disease.

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5. 11 points In a clinical study, volunteers are tested for a gene that has been found 5 to increase the risk for a disease. A person carries the gene with probability 0.12 independently of others. (a) Find the probability that four or more people will have to be tested before the first one with the gene is detected. (b) Given that more that 3 people have been tested without the gene detected find the probability that the gene is still not detected after 6 more people

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