Studies show that about one woman in seven (approximately 14.3%) who live to be 90 will develop breast cancer. Suppose that of those women who develop breast cancer, a test is negative 2% of the time. Also suppose that in the general population of women, the test for breast cancer is negative about 85% of the time. Let B = woman develops breast cancer and let N = tests negative. Suppose one woman is selected at random.
- What is the probability that the woman develops breast cancer? What is the probability that woman tests negative?
- Given that the woman has breast cancer, what is the probability that she tests negative?
- What is the probability that the woman has breast cancer AND tests negative?
- What is the probability that the woman has breast cancer or tests negative?
- Are having breast cancer and testing negative independent events?
- Are having breast cancer and testing negative mutually exclusive?
OpenStax Introductory Business Statistics 2e, 3.3 Two Basic Rules of Probability, exercise 8