Probability (no idea of the kind, and how to do it)

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Homework Statement



Peter and Paul bet one dollar each on each game. Each is willing
to allow the other unlimited credit. Use a calculator to make a
table showing, to four decimal places, for each of p = 1/10, 1/3,
.49, .499, .501, .51, 2/3, 9/10 the probabilities that Peter is ever
ahead by $10, by $100, and by $1000.



Homework Equations





The Attempt at a Solution



I don't know what to apply here. Thank you very much for any help!
 
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What random variable would it be appropriate to define?
 
Thank you for reply, rochfor.
I don't know what p is referring to. If p is the probability of winning a game, I don't know whose player the p is.
 
I imagine p is the probability of winning a game. I imagine wherever you got the problem from is a bit more explicit about which player's probability it is.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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