sdvr,
While it's true that each event occurs separately, since the question is what is the chance that "at least one win occurs" you have to looks at all of the probabilities combined.
As has been mentioned there are two ways to do this if you think in simple coin flips terms.... Chance of 1 heads in 4 flips, or chance of NOT all 4 flips being tails.
Most statisticians will say the 2nd is easier then the first... here's why.
One could work out all the separate cases – one head in four tosses, two heads, or three or four. H,H,H,H or H,H,H,T, or H,H,T,T .... etc until T.T.T.H
But it's much easier to find the probability of no heads, and subtract that from one: or not T,T,T,T
In our case Pr (at least one win in 4 cases) = 1 – Pr (no wins in 4 cases) = 1 – (0.8)4 = 59.04%.
Since you have to look at all events, the number isn't just 20% as you start losing cases and then move to level, your next 20% chance is basically taking 20% of the 80% failure to get a L,W scenario.
Hope that helps a bit.