B — the deploy claim. The other three all describe repeatable situations: flip the coin a thousand times, sample a thousand widgets, roll the dice all night. “Last night’s deploy caused this outage” happened exactly once. There is no ensemble of reruns; the claim is simply true or false, and you don’t know which. A long-run frequency reading has nothing to attach to.
Yet “60% it was the deploy” is obviously meaningful — you act on numbers like that constantly. You check the deploy log before the load balancer config. You’d bet a lunch on it, but not a paycheck. That number is a degree of belief: a summary of how plausible the claim is given everything you currently know.
Two things make this more than hand-waving:
- Degrees of belief obey the probability rules. There’s a classic result (associated with Cox and de Finetti — no need to memorize the names) showing that if your uncertainty numbers violate the probability axioms, you become incoherent in a very practical sense: someone can assemble a set of bets, each of which you’d individually accept, that loses you money no matter what happens. Coherent uncertainty is probability. Same math, wider scope.
- A belief is a bet. “60%” isn’t decoration — it commits you. It says which side of 3:2 odds you’d take, whether checking the deploy log is worth ten minutes, whether to roll back first and investigate second. If a number wouldn’t change any decision at any stakes, you haven’t really assigned it.
The common pitfall is the reverse of this lesson: hearing “there’s no probability here, it either happened or it didn’t.” True for the event; irrelevant for the reasoning. Probability in the Bayesian reading lives in your information about the world, not in the world itself. The coin on the floor under the couch is already heads or tails — your 50% describes you.
Where this goes: if beliefs are probabilities, then learning something new should move them in a lawful way. The rule for moving them is conditioning — the subject of the next lessons — and the whole track is about one loop: belief in, evidence in, updated belief out.