P(3) = 1 − 0.1 − 0.3 − 0.2 = 0.4.
The die’s true face-3 rate is the most plausible single value on the whole sheet — more plausible than any other individual face, though still short of “certain” (0.4, not 1.0).
Why this is a bigger idea than it looks. Every earlier lesson in this track secretly used a two-row version of exactly this table: “has disease” plausibility and “doesn’t have disease” plausibility, always summing to 1 (prior odds and posterior odds were just a different way of writing that same pair of numbers as a ratio instead of two summands). A pmf generalizes that same “answer sheet” idea from two rows to however many rows the question has — four die faces here; in a few lessons, every possible underlying success-rate from 0% to 100% for a coin.
The reframe worth sitting with: a distribution isn’t a description of one hypothesis with a confidence attached — it’s tracking a whole population of mutually exclusive hypotheses simultaneously, each with its own plausibility, all of them adding up to one certainty pooled across all of them. “The rate is probably around 30%, but I’m not ruling out 25% or 35%” isn’t a vague hedge — it’s an actual, precise answer sheet with a number written next to every candidate rate. That’s the object Stage 2 is going to build tools to update from data.
Where this goes: next lesson asks the natural follow-up — given some observed data (say, a coin flipped a few times), which values on an answer sheet like this one does that data actually favor? That’s the likelihood, the second ingredient (alongside the prior) in every Bayesian update you’ve done so far, now made explicit as its own object.