Question: A test for the presence of a certain disease has probability .05 of giving a false-positive reading (a positive test for a healthy person) and probability .03 of giving a false-negative result. Suppose that four individuals are tested, two of whom have the disease and two of whom do not. Let X = the number of positive readings.

a) Does X have a binomial distribution? Explain your reasoning.

b) What is the probability that at most two of the four test results are positive?