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Conditional probability mass function of the sum of independent geometric random variables.

$X, Y \sim Geom\left(p\right)$, and $X, Y$ are independent. Find $p_{X | X+Y}\left(i | n\right)$. My approach: pmf of geometric distribution: $p_X(i) = {p(1-p)^{i-1}}$ Then, by the law of total probability: $p_{X | X+Y}\left(i | n\right) = \frac{p_{X, X+Y}\left(i,n\right)}{p_{X+Y}\left(n\right)}$ [Is using the law of total probability here correct as opposed to using Bayes theorem?] […]