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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 non-caniers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual.
(a) Draw a probability tree that describes this experiment. Be sure to carefully de?ne your notation and write the joint probabilities at the end of each branch.
(b) What is the probability that both tests yield the same result?
(c) If both tests are positive, what is the probability that the selected individual is a carrier?
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