Studies show that approximately one woman in seven who live to be 90 will develop breast...
Studies show that approximately one woman in seven who live to be 90 will develop breast cancer. Assume that of those women who develop breast cancer, a test for breast cancer is negative 2% of the time (i.e., false negative). Also, assume that the test for breast cancer is negative 85% of the time.
a) What is the probability that a randomly chosen woman develops breast cancer?
b) What is the probability that a randomly chosen woman tests negative for breast cancer?
c) What is the probability that a randomly chosen woman has breast cancer and tests negative for breast cancer?
d) What is the probability that a randomly chosen woman has breast cancer or tests negative for breast cancer?
Homework Answers
| Test positive | Test negative | Total | |
| Develop breast cancer | 0.1429 - 0.00285 = 0.139942 | 0.1429 X 0.02 = 0.002858 | 1/7=0.1429 |
| Do not develop breast cancer | 0.15 - 0.139942 = 0.010058 | 0.847042 | 1 - 0.1429 = 0.8571 |
| Total | 1 - 0.85 = 0.15 | 0.85 | 1.00 |
(a)
P(Develop breast cancer) = 0.1429
(b)
P(Test negative) = 0.85
(c)
P(Develop breast cancer AND Test negative) =
0.002858
(d)
P(Develop breast cancer OR Test negative) = P(Develop breast
cancer) + P(Test negative) - P(Develop breast cancer & test
negative) = 0.1429 + 0.85 - 0.002858 =
0.9900422
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