Does a positive mammogram mean cancer?

Tumors are often associated with Cancer but actually, most tumors are not cancerous. A tumor caused by cancer is considered malignant, while non-cancerous tumors are considered benign. When examining breast tumors, doctors have found only about 1 in 100 breast tumors are malignant.

Now, suppose a mammogram test comes back positive but has only an 85% accuracy rate (meaning it will correctly identify 85% of malignant tumors).

• What do you think chance is that the person has cancer if the test came back positive?

Initial Post:

Step 1: We will be creating a table to represent the possible outcomes the person has cancer and results from the test. We will assume there are 10,000 women in the study. Please fill out the table as we find the possible results. Please refer to the last slide of Topic 18 PowerPoint on Basics of probability for false positives, true positives, false negatives and true negative tests.

• If we have 10,000 women in the study with tumors and only 1% are malignant, how many women do we expect to actually have cancer? 10000*.01 = ? This will be the total number of malignant tumors.
• How many do we expect to not have cancer? 10000*.99 = ? This will be the total number of benign tumors.
• Since the mammogram test is only 85% accurate, how many of the malignant tumors will come back with a positive mammogram? .85*100 = ? This will be the number of true positive tests.
• How many of malignant tumors will come back with a negative mammogram? .15*100 = ? This will be the number of false-negative tests.
• How many of the benign tumors will result in a negative mammogram? .85*9900 = ? This will be the number of true negative tests.
• How many of the benign tumors will result in a positive mammogram? .15*9900 = ? This will be the number of false-positive tests.
• Find the total number of positive and negative mammograms and fill in the total row.