Chapter 6.6, Problem 11E

Exercises 11–15 refer to diagnostic tests. A false negative in a diagnostic test is a test result that is negative even though the patient has the condition. A false positive, on the other hand, is a test result that is positive although the patient does not have the condition.

Mammogram Accuracy The New York Times of January 24, 1997, discussed the recommendation of a special panel concerning mammograms for women in their 40s. About 2% of women aged 40 to 49 years old develop breast cancer in their 40s. But the mammogram used for women in that age group has a high rate of false positives and false negatives; the false positive rate is .30, and the false negative rate is .25. If a woman in her 40s has a positive mammogram, what is the probability that she actually has breast cancer?