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Algorithmic Learning Based On Statistics And

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2. A new mammography test kit is devised to screen for breast cancer. The
manufacturer of the kit states that 90% of women who do have breast
cancer 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% of
women who are referred by doctors to take this test (for example, because
they saw unusual lumps in their breast) do have breast cancer.
2
2a) A woman has tested positive. What is the probability that she has
breast cancer?
2b) A nice feature of this test is that applying it to the same patient several
times, then the outcome of each test is independent of previous results.
So if a person who does not have cancer tests positive, the chances
of her testing positive on a subsequent test remains 9%. If a patient
tests positive for the first time and tests positive again for the second
time, 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?Statistics and Probability