Accuracy of pregnancy tests. Sixty percent of all women who submit to pregnancy tests are really pregnant. A certain pregnancy test gives a false positive result with probability .03 and a valid positive result with probability

.98. If a particular woman’s test is positive, what is the probability that she really is pregnant? [Hint: If A is the event that a woman is pregnant and B is the event that the pregnancy test is positive, then B is the union of the two mutually exclusive events A ¨ B and Ac ¨ B. Also, the probability of a false positive result may be written as P1B0Ac2 = .03.]