Most people who have been exposed to probability and statistics have come across Bayes’ Formula, but I suspect that many have not fully understood and internalized what the formula tells us. This is unfortunate because, as we will see, the formula applies to situations where our intuition about probability can lead to wildly incorrect judgments. What is more, those situations often involve critical issues, such as interpreting the results of medical tests.
The importance of the formula is such that a whole branch of thought in science and statistics, Bayesian inference, or Bayesianism, springs directly from the formula and its implications.

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