You can do an average if you have equally-likely events. But that's really the same as multiplying by the probability. For example, the average of five value is:
(a + b + c + d + e)/5
....right? That's the same as (1/5)*a + (1/5)*b + (1/5)*c + (1/5)*d + (1/5)e. If all five outcomes are equally likely, that's the probability 1/5 times each one, added up.,
If the outcomes were not equally-likely, you wouldn't expect the same result, though, would you? Multiplying each outcome value by the probability, rather than 1/n, has the effect of "weighting" the average to account for the different likelihoods.