2. Human Chorionic Gonadotropin (hOG) pregnancy tests or home pregnancy tests de- termine pregnancy through the detection of the hormone hCG in a woman's urine. Tests too soon after conception can result in false negatives and certain aspects of recent health history of a women can result in false positives. Let A be the event tests positive and ( be the event woman is pregnant. (a) Given a false positive rate of 2% and a false negative rate of 6%, find P(AJC) and P(A| C ). (b) Find the probability that a woman tests positive if her assessment that the prob- ability that she is pregnant is 75%. (c) Use the information above to find the probability that a women is pregnant given that she tests positive. (d) Determine this conditional probability if her assessment that the probability that she is pregnant is reduced to 25%