What does Bayes' Theorem say in plain English?



What does Bayes’ Theorem mean? What do the different parts of the equation say in plain language?


Let’s first recall that Bayes’ theorem is stated as follows

P(A|B) = P(B|A) * P(A) / P(B)

In plain language, Bayes’ theorem is saying

If we know that B is true and would like to find when A is also true, we should

  • focus our attention on the outcomes where B is true
  • and then once focused there, look at all the outcomes in this area where A is true.

The first point first. Since all probabilities are between 0 and 1, if we consider the number 1 to mean all possible outcomes, then P(B) means all outcomes where B is true. So this is where the denominator of P(B) in the equation comes from.

For the second point, we’re asking here about the intersection of A and B which we can write as P(B|A) * P(A), explaining the numerator of the equation.