## Assume that the probability of breast cancer equals

Assume that the probability of breast cancer equals
Assume that the probability of breast cancer equals .01 for women in the 50–59 age group. Furthermore, if a women does have breast cancer, the probability of a true
positive mammogram (correct detection of breast cancer) equals .80 and the probability of a false negative mammogram (a miss) equals .20. On the other hand, if a women
does not have breast cancer, the probability of a true negative mammogram (correct non detection) equals .90 and the probability of a false positive mammogram (a false
alarm) equals .10. (Hint: Use a frequency analysis to answer questions. To facilitate checking your answers with those in the book, begin with a total of 1,000 women,
then branch into the number of women who do or do not have breast cancer, and ?nally, under each of these numbers, branch into the number of women with positive and
negative mammograms.)

(a) What is the probability that a randomly selected woman will have a positive mammogram?