a+ b is a binomial because it has two parts. The actual "binomial theorem" has nothing to do with probability and its name has nothing to do with "outcomes".
Taking Statistics for Economists, and the book refers to the binomial theorem using as:
where n is # of Bernoulli trials.
I just realized though, although this is considering p(success) and p(failure) as the variables, since outcome space is also a variable, would not a more appropriate moniker be trinomial theorem? I do not know if this qualifies as a question or not, just looking for some clarification on the terminology since number of trials can be potentially infinite.