Here's a story problem about a situation that doctors often encounter:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

What do you think the answer is? If you haven't encountered this kind of problem before, please take a moment to come up with your own answer before continuing.

If you think it would help, make like a constipated mathematician.

If you get the answer wrong, you're *irrational*.

If you click here [2] to find the correct answer, you're both *irrational* and *lazy*.

(Judge not, that ye be not judged? Yeah, I already worked out the correct answer myself, thanks. )