$X_1, X_2, X_3$ iid with geo(p) distribution Find the distribution of $X_1|X_1+X_2$.
$$P(X_1=k|X_1+X_2=n)=...=\frac{p^2(1-p)^n}{P(X_1+X_2=n)} $$
It's independent from k, so it will be uniformly distributed.
The answer is $U(\{0,1,2,...,X_1+X_2\})$ - what I don't understand is why the last value is $X_1+X_2$.