Question

Breast cancer occurs most frequently among older women. Of all age groups, women in their 60s have the highest rate of breast cancer. It is estimated that 3.7% of women in their 60s get breast cancer. Mammograms are X-ray images of the breast used to detect breast cancer. A mammogram can typically identify correctly 84.9% of cancer cases (sensitivity = 84.9%) and 95.13% of cases without cancer (specificity = 95%). (This is exactly like problem #11)

First write down the probabilities given in the question and then answer the following questions

[3] b. Sally who is in her 60s gets a mammogram. What is the probability that she will test positive for breast cancer?

c. Suppose Sally tests positive for breast cancer, what is the probability that she actually has the cancer?

Answer 1

b)

P(tested positive)=P(have breast cancer and tested positive)+P(not have breast cancer and tested positive)
	=0.037*0.849+(1-0.037)*(1-0.9513)=0.0783

c)

P(have breast cancer|tested positive)=0.037*0.849/0.0783=0.4011