This seems to me to be the best way to understand Bayes&#x27; theorem, with natural frequencies being the best way to mentally compute with it. E.g. for the breast cancer example,<p>- Imagine there are 1000 women who participate in routine screening<p>- 1% → 10 of these have breast cancer<p>- 80% → 8 of these will get positive mammograms<p>- 990 don&#x27;t have breast cancer<p>- 9.6% ≅ 10% → 99 of the 990 get positive mammograms<p>So that the probability of having breast cancer, given a positive mammogram, is ≅ 8&#x2F;99 ≅ 8%.<p>There is a bunch of research on natural frequencies being generally the best way to reason about this sort of thing.