I don't know where to begin with this one....

When told that over a 10-year period a mammogram test has a false positive rate of 50 percent, Bob said "That means that about half the women tested actually have no cancer". Correct Bob's mistaken interpretation.

What about the women that tested negative for cancer?

Bob's interpretation is incorrect. The false positive rate of a mammogram test refers to the proportion of test results that are positive for cancer but are actually false alarms, meaning the woman does not have cancer. In other words, when the test result is positive, it does not necessarily mean that the woman has cancer. The false positive rate does not indicate how many women actually have no cancer.

To understand this better, let's look at an example: if 1,000 women took the mammogram test and the false positive rate is 50 percent, it means that 500 women would receive a positive test result even though they do not have cancer. However, it does not say anything about how many women in the group actually have cancer.

To accurately determine the number of women who have cancer, we need to consider the sensitivity (true positive rate) of the test, which measures the proportion of women who have cancer and are correctly identified by the test. The false positive rate and sensitivity go hand in hand to assess the accuracy of the test.