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Storm Warning...
Cheap shot!! Accurate, but none the less cheap ;->
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A math problem most doctors got wrong:
About 1 per cent of women have breast cancer and a cancer screening method can detect 80 per cent of genuine cancers but also has a false-alarm rate of 10 per cent. What is the probability that women producing a positive result really have breast cancer? Most doctors reckoned it was at least 70 per cent.
The correct answer, found by only two doctors, is just 8 per cent.
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Re: A math problem most doctors got wrong:
Picture an initial sample of 1000 women. 10 have breast cancer. Out of the 990 who do not, the 10% false alarm rate means the test will show 99 positives. Out of the 10 women who have breast cancer, the 80% detection rate means the test will show 8 positives. So, after testing 1000 women the test shows 107 positives. Only 10 women have breast cancer, but only 8 of the positive test patients have breast cancer. 8 out of 107 is 7.5% (or, more precisely, but still not exact: 7.48%).
Nit-picking, I know. But as long as you're talking about getting a math problem wrong...
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Re: A math problem most doctors got wrong:
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Classic errors and fallacies
That said, a senior professor very publicly got a related problem wrong as an expert witness in the UK, and more than a dozen women were wrongly jailed for their cot death babies.....
but then the same problem is taught as the cause of a classic fallacy in law school, so the defence lawyers and presiding judges have something to explain too...
The false storm warning is a different classic error : not checking your sources. Something which matters ever more when sites crib from each other, the net can become an engine of misinformation
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