1. 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?
2. A system consists of two components. The proba- bility that the second component functions in a sat- isfactory manner during its design life is .9, the probability that at least one of the two components does so is .96, and the probability that both components do so is .75. Given that the rst component functions in a satisfactory manner throughout its de- sign life, what is the probability that the second one does also?