Probability tree - probabilities and values of each branch

Dear Matlab community,

I found a somewhat related post, but it is not quite the same, so I decided to start a new post.

The problem: I am looking at a probability tree: Stage one: The price of a stock is initially $50 In each round, the price can change

(-3,-2,-1,0,+1,+2,+3), so we are looking at seven possible changes.

The probabilities for those events are static, and known:

(0.08,0.14,0.22,0.3,0.14,0.08,0.04), and price changes are independent for each round of changes.

Required:

• all possible prices of the stock after 20 rounds, and
• the probability for each of those prices after 20 rounds.

I would much appreciate your help! Thank you very much in advance!