I think this is a binomial question because it involves success/failure (win/lose) but it doesn't give that information. I'm finding this question difficult because it asks for the probability of winning $x$ games. I'm more comfortable with examples using actual numbers rather than "$x$ games".
Q: There is a $7$ game tournament between player $A$ and $B$. Player $A$ has $0.6$ chance of winning each game. Find the probability player $A$ wins the tournament in $x$ games.
So if its binomial then I'll have $p=0.6$ and $q=0.4$. Player $A$ would need to win $4$ games before s/he has won the tournament so $x$ must be $x=4,5,6,7$. So what is $n$? How do I write out my pdf for this problem? Thanks very much.