One percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 90% detection rate for carriers and a 5% detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual.
a. What is the probability that both tests yield the same result?
b. If both tests are positive, what is the probability that the selected individual is a carrier?
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