A test for the presence of a certain disease has probability .20 of giving a false-positive reading (indicating that an individual has the disease when this is not the case) and probability .10 of giving a false-negative result. Suppose that ten individuals are tested, five of whom have the disease and five of whom do not. Let X = the number of positive readings that result.
a. Does X have a binomial distribution? Explain your reasoning.
b. What is the probability that exactly three of the ten test results are positive?
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