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And the answer is...

Posted By: tansley
Date: Wednesday, 30 July 2008, at 9:21 p.m.

In Response To: More probability (tansley)

The probability that the woman has cancer is 1/12, or 8.33%, as Sean and others identified. Indeed Sean's subsequent explanation (the one not using Bayes' theorem) is exactly the same as mine, so I'll simply quote it here:

Assume 1000 women are tested. 990 do not have cancer. 10 do. Of the 990 who don't 99 will test positive. Of the 10 who do 9 will test positive. So you get 108 positive results. 9 of these are genuine. 9/108 = 0.083 So the probability that the woman has cancer if she tests positive is 8.3%

Alarmingly when this question was put to twenty-four physicians working in the field (breast cancer, as it happens), two got it right. Two more were close, but for the wrong reasons. The rest were wrong; in most cases very very wrong. These are the people who will interpret the test results, should you ever have a positive test. Let's hope their medical skills are better than their numeracy!

tansley

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