Which probability is larger for a randomly selected woman from the general population: The probability of having breast cancer given that the woman has a positive mammogram, or the probability of a positive mammogram given that the woman has breast cancer?
A)The probability of having breast cancer given that the woman has a positive mammogram.
B)The probability of a positive mammogram given that the woman has breast cancer.
C)The probabilities are the same.
D)Not enough information to tell.

Question

Quizplus · Accepted Answer

The probability of a positive mammogram given that the woman has breast cancer is generally higher because it reflects the sensitivity of the mammogram test (how likely the test is to correctly identify cancer when it is present). The probability of having breast cancer given a positive mammogram is affected by the overall prevalence of breast cancer in the population and the specificity of the test (how likely the test is to correctly identify no cancer when it is not present), which can result in a lower probability due to false positives.

Which Probability Is Larger for a Randomly Selected Woman from the General