1) Two percent of woman of age 45 who participate in routine screening have breast cancer. Ninety percent of those with breast cancer have positive mammographies. Ten percent of the women who do not have breast cancer will also have positive mammographies. Given a woman has positive mammography, what is the probability she has breast cancer? Explain the steps.

2) Let A, B, C be events such that P(A) = .2, P(B) = .3, P(C) = .4. Find the probability that at least one of the events A and B occurs if (a) A and B are mutually exclusive (b) A and B are independent Find the probability that all of the events A, B, C occur if (a) A, B, C are independent (b) A, B, C are mutually exclusive