Question 1040583: Studies show that, if she lives to be 90, about 1 woman in 7 (approximately 14.3%) 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.
a. What is the probability that the woman develops breast cancer? What is the probability that woman tests negative?
b. Given that the woman has breast cancer, what is the probability that she tests negative?
c. Given that the women tests negative, what is the probability that she has cancer?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Table with 7000 women.
=======Will develop=======will not develop======total
Test++=====980==============70==========1050
Test--======20=============5930==========5950
Total--------1000-----------------6000-------------7000
The probability she develops breast cancer is 14.3%
The probability that a random woman tests negative is 85%
Given she has cancer (1000), probability she tests negative is 2%
Given that she tests negative (5950 women), the probability that she has cancer is 20/5950 or 0.33%
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