193 Accuracy of pregnancy tests. Seventy-five percent of all women who submit to pregnancy tests are really pregnant.

A certain pregnancy test gives a false positive result with probability .02 and a valid positive result with probability

.99. 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 P1BAc2 = .02 .]