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I'm currently having a lot of trouble with this probability problem. For example:

Suppose there are 5 balls in a bag with number 1,2,3,4,5. I pick a ball at random 20 times (with replacement).

Lets say the probability of each ball being picked is:

P(1) = 0.5

P(2) = 0.15

P(3) = 0.1

P(4) = 0.2

P(5) = 0.05

After I pick the ball 20 times, I sum it up. The sum is denoted as T.

I want to find the probability that T>=50. How do I go about doing this?

I'm not entirely sure if this actually links to sample space. Sample space is just something that I have in my mind. I've seen sample space where there are 2 variables, but what about more than 2?

Any help would be appreciated

Thanks