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  title: '"I'm confused, and surely wrong, about the cance..."',
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  text: 'I'm confused, and surely wrong, about the cancer example.\n\n1 in 10000 people are sick.  1 sick person : 9999 well persons\nmultiply by 100: 100 sick people : 999900 well persons\n99% of the sick people have positive tests:  (0.99 * 100 = ) 99 Positive tests \n 1% of the well people have false positive tests: (0.01 * 999900 = 9999)\n\nUsing the odds view: number of sick persons with positive tests / total number of persons with positive tests: (99 / (99 + 9999) = 99 / 10098.  Multiply top and bottom by (1/99) => (99/99) / (10098/99) = 1 / 102.  The text says the answer is 1 / 101.010101... which is 99/10000.\n\nSo, try the waterfall method.\n\nprior odds of being sick: 1 in 10000.\nBeing sick: 1\nBeing well: 9999\n\nchance of having positive test while sick: 99\nchance of having positive test while well: 1\n\nodds of being sick given positive test: (1 / 9999) * (99 / 1) = 99 / 9999 = 0.00990099\nprobability of being sick given positive test: 99 / (99+9999) = 1 / 102 from above.\n\nWhere did I go wrong?  Thanks in advance for any time you have!',
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