Statistics Done Wrong
Isn't most or all of this avoided by explicitly using Bayes' theorem along with a correct formalization of the domain?E.g. for the mammogram:P(cancer) = 0.8%P(~cancer) = 1 - P(cancer) = 99.2%P(positive_mammogram | cancer) = 90%P(positive_mammogram | ~cancer) = 7%P(cancer | positive_mammogram) = P(positive_mammogram | cancer) P(cancer) / (P(positive_mammogram | cancer) P(cancer) + P(positive_mammogram | ~cancer) (1 - P(cancer))) = 90% * 0.8% / (90% * 0.8% + 7% * 99.2%) = 9.39457%