More Accurate Mammograms. Like Table 3.7, the following table is based on the assumption that 1% of breast tumors are malignant. However, this table assumes that mammogram screening is 90% accurate (versus 85% accurate, as assumed in Table 3.7).
Tumor Is Malignant | Tumor Is Benign | Total | |
Positive Mammogram | 90 true positives | 990 false positives | 1080 |
Negative Mammogram | 10 false negatives | 8910 true negatives | 8920 |
Total | 100 | 9900 | 10,000 |
a. Verify that the numbers in the table are correct.
b. Suppose a patient has a positive mammogram. What is the chance that she really has cancer?
c. What is the chance of a positive mammogram, given that the patient has cancer?
d. Suppose a patient has a negative mammogram. What is the chance that she actually does have cancer?
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