Studies show that about one woman in seven (approximately 14.3%) who lives 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 be the event a woman develops breast cancer and let  be the event a woman tests negative for breast cancer. Suppose a woman is selected at random.

MATLAB: An Introduction with Applications
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  1. Studies show that about one woman in seven (approximately 14.3%) who lives 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 be the event a woman develops breast cancer and let  be the event a woman tests negative for breast cancer. Suppose a woman is selected at random.
    1. What is the probability that she develops breast cancer?
    2. What is the probability that she tests negative?
    3. Given that she has breast cancer, what is the probability that she tests negative?
    4. What is the probability that she has breast cancer and tests negative?
    5. Are having breast cancer and testing negative independent events?
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