The probability of breast cancer is 1% for women at age forty who participate in routine screening. If a woman has breast cancer the probabilty is 80% that she will get a positive mammography. If a woman does not have breast cancer, the probability is 9.6% that she will also get a positive mammography.

A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

10 out of every 1000 women at age forty, who participate in routine screening have breast cancer. 8 out of every 10 women with breast cancer will have a positive mammography. 950 out of every 990 women without breast cancer will also have a positive mammography.

Here is a sample of women who have a positive mammography. How many of these women actually have breast cancer?

**Create a 2x2 table for the mammogram problem. **

Calculate

1. Probability of having breast cancer. p(BC).

2. Probability of having BC given the mammogram is positive. p(BC/positive mammo)

3. Probability of having a positive mammogram given a person has BC. P(pos mammo/BC)

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