Suppose mammograms are used to screen for breast cancer in a particular city, an
ID: 3061631 • Letter: S
Question
Suppose mammograms are used to screen for breast cancer in a particular city, and the following information is known.
What if the prevalence of breast cancer was 15%?
If a woman has breast cancer, the probability that the mammogram is positive is 90%. (sensitivity)
If a woman does not have breast cancer, the probability that the mammogram is positive is 9%. (false-positive rate)
Use the table approach to determine the proportion of those testing positive that actually have breast cancer.
When answering this question, please construct a table.
Thank you in advance for helping me.
Explanation / Answer
P(breast cancer) = 0.15
P(mammogram is positive | has breast cancer) = 0.9
P(mammogram is positive | deos not have breast cancer) = 0.09
P(mammogram is positive) = P(mammogram is positive | has breast cancer) * P(breast cancer) + P(mammogram is positive | deos not have breast cancer) * P(no breast cancer)
= 0.9 * 0.15 + 0.09 * (1 - 0.15)
= 0.2115
P(have breast cancer | testing positive) = P(mammogram is positive | has breast cancer) * P(breast cancer) / P(mammogram is positive)
= 0.9 * 0.15 / 0.2115
= 0.6383