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I managed to reach the correct (I think) answer without Google, the comments, or any knowledge of the Bayes' Theorem using the following method:
0.8% of women get positive mammographies and have breast cancer
9.696969696969697% of women get positive mammographies and don't have breast cancer
0.8 + 9.696969696969697 = 10.496969696969697
Therefore, 10.496969696969697% of women get positive mammographies
As 0.8% of women get positive mammographies and have breast cancer, we simply need to calculate what percentage 0.8 is of 10.496969696969697
Therefore, there is a 7.621247113163973% chance that a woman with a positive mammography has breast cancer.
An Initiate of the Bayesian Conspiracy
An Intuitive Explanation of Bayesian Reasoning is an extraordinary piece on Bayes' theorem that starts with this simple puzzle: 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 with...
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Jan 12, 2011
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