Geometric Distribution

$X \sim Geom(p)$

$P(X=x)=(1-p)^x p$

where:

$0 \lt p \le 1 $ - is the success probability
$x \in \{ 0, 1, 2, \ldots \}$ - is the number of failures before the first success

$\mathrm{E}[X]=\dfrac{1-p}{p}$

$\mathrm{Var}[X]=\dfrac{1-p}{p^2}$

$GeomII(p)$ - where $x \in \{ 1, 2, \ldots \}$ is the number of trials to get one success (including the first success). Its probability mass function is $P(X=x)=(1-p)^{x-1} p$.