If E(X) = n*p, wouldn't that make the answer 5 x 0.6, which is 3?

Mr F says: It's not Binomial, forget that idea. It's negative binomial, as I said in my earlier post.
I don't understand where the 8.33 is coming from - where did you get the 25 from in order to divide it by 3?

All my book says is that

(there's supposed to be a y under the sum symbol, but I don't know how to do that). Then there's a lot of steps to follow, and at the end, it ends up being

. It's not very clear, I have no idea what it's talking about. I took an advanced probability class in grade 12, and the textbook was really clear and I actually understood most of it, but this year I'm completely lost. I know it's university so it's supposed to be harder, but it just seems like the textbook moves too quickly and includes limited examples, so I'm confused most of the time.

I'm sorry, I don't understand. Where did the 20 and the 6 come from?