Geometric Distribution

Counting trials until first success (support $k=1,2,\dots$) with success probability $p\in (0,1)$:

$$P(X=k)=(1-p{)}^{k-1}p$$

Expected Value

$$\mathbb{E}[X]=\frac{1}{p}$$

Variance

$$\mathrm{Var}(X)=\frac{1-p}{p^2}$$