Waiting for a Rare Success

The number of trials until the first success follows a geometric distribution.

The mean of Geometric$(p)$ on $\{1,2,\dots \}$ is $1/p$.

1. 1. Apply the geometric mean formula

   For success probability $p=0.2$, the expected waiting time is $1/p$.

   $$E[T]=\frac{1}{0.2}=5$$

Answer: 5