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**jjbrian** Peter has probability 1/4 of winning each game. Peter and Paul each bet $100 on each game. They each start with $400 and play until one of them goes broke. What is the probability that Paul goes broke?

Ans: 0.01220

How do you do this problem>?

I used this formula:

Suppose Peter starts with s dollars and Paul starts with t-s dollars. Let P* be the probability that Peter wins all the money. Then

P* = (1 -r^s) /(1-r^t)

where r = q/p (p not equal q).

Attempt:

s = 400 (Given)

t = 800 (from t-400= 400)

p = 1/4 (Given)

q = 3/4 (q=1-p) = (1-1/4)

r = 3 (q/p)