Hey just toss it

Let be $X$ the random variable that gives us the number of tails after a first head. Given that $\mathbb{P}(\text{tail})=\frac{19}{20}$ and $\mathbb{P}(\text{head})=\frac{1}{20}$ , $\mathbb{P}(X)$ is

$\displaystyle \mathbb{P}(X=n)=\bigg(\frac{1}{20}\bigg)\bigg( \frac{19}{20}^n\bigg)$ .

The expected value of $X$ is

$\displaystyle \mathbb{E}[X=n]=\sum_{n=1}^{+\infty} n \bigg(\frac{1}{20}\bigg)\bigg( \frac{19}{20}^n\bigg)=\boxed{19}$