Here is Bayes' Rule: P(Q | G) = [P(Q) x P(G|Q)] / ([P(Q) x P(G|Q)] + [P(not Q) x P(G|not Q)]) Use Bayes' Rule, which means you need to show your work, in order to solve the following problem: Mary and her husband have been trying to have a baby, and she suspects that she is pregnant. She takes a pregnancy test that has a true positive rate of 0.99 (i.e., 99 percent of the time it indicates that a pregnant woman is pregnant) and a false positive rate of 0.02 (i.e., 2 percent of the time it indicates that a woman who is not pregnant is pregnant). Suppose further that 20 percent of all women who take this pregnancy test are indeed pregnant. (1) Given that the test was positive, how likely is it that Mary is pregnant