Assign a number to each of those events (having 1 as outcome, having 2 as outcome, ..., having 20 as outcome) which is the job of Random Variable. For this specific example, we can assign the same numbers. The Expected Value equation is μ=∑x.p(x). Now you have x=1,2,...,20, and if you have p(x), you can easily calculate expected value.
In this case that we have a fair die with 20 sides, probability of each side is 120. Now, we can calculate it in this way:
μ=∑x.p(x)=∑20x=1x.120=120∑20x=1x=12020×212=10.5
(note: ∑nx=1x=n×(n+1)2)