06: Problem 15 Previous Problem Problem List Next Problem (2 points) To determin
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06: Problem 15 Previous Problem Problem List Next Problem (2 points) To determine whether or not they have a certain desease, 324 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to group the people in groups of 18. The blood samples of the 18 people in each group will be pooled and analyzed together. If the test is negative, one test will suffice for the 18 people (we are assuming that the pooled test will be positive if and only if at least one person in the pool has the desease); whereas, if the test is positive each of the 18 people will also be individually tested and, in all, 19 tests will be made on this group. Assume the probability that a person has the desease is 0.1 for all people, independently of each other, and compute the expected number of tests necessary for the entire group of 324 people answer:Explanation / Answer
probabilty that there is no diseased in 18 people group =(0.9)18 =0.1501
hence for a group expected tests=19*probability of test positive+1*probability of test negative
=19*(1-0.1501)+1*0.1501 =16.2982
therefore expected number of test necessary for 18 groups =18*16.2982 =293.37
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