Question

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?

Answer 1

	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