A PCR test for COVID yields false negatives with probability 0.05 and rarely yields false positives (assume 0). Let p be the probability that an individual contracted COVID. (a) Find the expression for the probability of getting a negative test. (b) Find an expression for the probability of being infected given a negative test. (c) For 0 p 1, graph the conditional probability you found in (b) as a function of p. (d) Find the prior probability for which the probability of being infected given a negative test is 20%