5.58 More screening for breast cancer Refer to the previous exercise. For young women, the prevalence of breast cancer is lower. Suppose the sensitivity is 0.86 and the specificity is 0.88, but the prevalence is only 0.001.

a. Given that a test comes out positive, find the probability that the woman truly has breast cancer.

b. Show how to use a tree diagram with frequencies for a typical sample of 1000 women to explain to someone who has not studied statistics why the probability found in part a is so low.

c. Of the cases that are positive, explain why the proportion in error is likely to be larger for a young population than for an older population.