Answer
$P(20)=0.01989$
Work Step by Step
$P(x)=({}_{x-1}C_{r-1})p^r(1-p)^{x-r}$
$x=20$, $r=2$, $p=\frac{2}{2+18+18}=\frac{1}{19}$ and $1-p=\frac{18}{19}$
$P(20)=({}_{19}C_{1})(\frac{1}{19})^2(\frac{18}{19})^{18}=\frac{19!}{1!\times18!}\times\frac{18^{18}}{19^{20}}=\frac{18^{18}}{19^{19}}=0.01989$
