Suppose the probability of a false positive result on a mammogram is 4% and that radiologists' interpretations of mammograms are mutually independent in the sense that whether or not a radiologist finds a positive result on one mammogram does not influence whether or not the radiologist finds a positive result on another mammogram. Assume that a woman has a mammogram every year for ten years.
a) What is the probability that she will have no false positive results during that time?
b) What is the probability that she will have at least one false positive during that time?
c) What is the probability that she will have exactly two false positive results during that time?
d) Suppose that the probability of a false negative result on a mammogram is 2%, and assume that the probability that a randomly chosen woman has breast cancer is 0.0002.
i) If a woman has a positive test result one year, what is the probability that she actually has breast cancer?
ii) If a woman has a negative test result one year, what is the probability that she actually has breast cancer?