If a woman takes early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test negative, meaning that the test says she isn't pregnant. Assume that if the woman really is pregnant, there is a 95% chance that she will test positive. Also, assume that if a woman really isn't pregnant, there is a 98% chance that she will test negative.
(a) Suppose that 1000 women take early pregnancy tests and that 150 of them really are pregnant. Determine the probability that a randomly selected woman from this group will test negative?
(b) Suppose that the woman tests negative. Determine the probability that she is pregnant?