The words “falsifiable” and “testable” are sometimes used interchangeably, which imprecision is the price of speaking in English. There are two different probability-theoretic qualities I wish to discuss here, and I will refer to one as “falsifiable” and the other as “testable” because it seems like the best fit.
As for the math, it begins, as so many things do, with:
This is Bayes’s Theorem. I own at least two distinct items of clothing printed with this theorem, so it must be important.
To review quickly, B here refers to an item of evidence, is some hypothesis under consideration, and the are competing, mutually exclusive hypotheses. The expression means “the probability of seeing B, if hypothesis Ai is true” and means “the probability hypothesis is true, if we see