# Probability distribution problem

I need some help please with this question:

A player decides whether to stop playing or not just after the first loss -or- after 10 games.

the probability for winning a single game is p.

all the games are independent.

Let X be the amount of total games which the player Participated.

I'm trying to look for the distribution of X [P(X=k)].

I let k be the number of games and if k is not ten the distribution is (p^k-1)*(1-p)

k-1 victories and one loss, I just can't see how to Involve the 10 detail into this Equation.

Thank you.

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For $k \lt 10$ it should be $p^{k-1}(1-p)$. Please use parentheses (or, even better, $\LaTeX$) as exponentiation binds more tightly than subtraction –  Ross Millikan Apr 3 '11 at 18:15

You already know the formula for $\mathbb{P}(X=k)$ for $1\leq k\leq 9$.
The player plays a total of ten games if and only if the first nine games are all victories. So $\mathbb{P}(X=10)=p^9$.