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To determine whether or not they have a certain desease, 80 people are to have their...

To determine whether or not they have a certain desease, 80 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 16. The blood samples of the 16 people in each group will be pooled and analyzed together. If the test is negative, one test will suffice for the 16 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 16 people will also be individually tested and, in all, 17 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 80 people.

Math   Statistics-And-Probability   
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Answer:

=> E(X) = 1 *(0.9)^16 + 17*(1 - 0.9^16) = 14.035

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