(a) For women aged 40-65, the prevalence rate of breast cancer is 800 pet 100,000. A particular

diagnostic test is accurate for 85% of women with breast cancer and for 95% of women

who do not have breast cancer.

(i) The diagnostic test is positive for a particular woman. What is the probability that

she has breast cancer?(ii) Given a sample of n women, let X denote the number of women who have breats

cancer. State what the probability distribution of this random variable is, and justify

your answer.

(iii) If 10,000 women were tested, how many would you expect to have breast cancer?