Algorithmic learning based on statistics and

2. A new mammography test kit is devised to screen for breast cancer. Themanufacturer of the kit states that 90% of women who do have breastcancer test positive for the test. The test also has a 9% false-positive rate(that is 9% of women without breast cancer test positive.) About 8% ofwomen who are referred by doctors to take this test (for example, becausethey saw unusual lumps in their breast) do have breast cancer.22a) A woman has tested positive. What is the probability that she hasbreast cancer?2b) A nice feature of this test is that applying it to the same patient severaltimes, then the outcome of each test is independent of previous results.So if a person who does not have cancer tests positive, the chancesof her testing positive on a subsequent test remains 9%. If a patienttests positive for the first time and tests positive again for the secondtime, what is the probability that she has breast cancer?2c) A woman has tested negative for breast cancer. What is the proba-bility that she does not have breast cancer?