Consider a coin which comes up heads with probability $p$ and tails with probability $1-p$, where $0 < p < 1.$ Suppose we keep tossing the coin until we have seen both sides of the coin. What is the expected number of times we would have seen tails? (Hint: the expected number of tosses required to see heads for the first time is $(1/p.)$
- $\frac{1}{p}$
- $1+\frac{1}{1-p}$
- $p+\frac{1}{p}-1$
- $2$
- None of the above