Logic 101: Don't ask about the bronze rat

Richard Goode's picture
Submitted by Richard Goode on Fri, 2013-01-04 17:41


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 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. Smiling)

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Damien Grant's picture

Despite being very careful, double checking my results, and getting the theory right, I had the decimal point in the wrong spot so was out by a factor of ten.

Fail. I'm irrational. Damn.

I hate probabilities and statistics...

reed's picture

If you stretched all of the world's statisticians' molecules from the Earth to the Sun they still wouldn't reach a conclusion.

I got the right answer. It took a while to work out the bronze rat. I had to use a pencil in the end.


Richard Goode's picture

Yes, you're right. Smiling

Now, answer the question.

Is this question poorly

reed's picture

Is this question poorly worded or am I too pedantic? … don't answer that. Smiling

80% of women with breast cancer will get positive mammographies.

Should be...

80% of women at age forty who participate in routine screening who have breast cancer will get positive mammographies.

(Likewise for the 9.6% conditions.)

Otherwise the question can't be solved.


Richard Goode's picture

Don't put your actual answers in the comments either, thanks. Smiling

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