+785 In a series of coin flips, a run is a series of one or more consecutive coin flips that all have the same result. For example, in the sequence
\[TT \textcolor{red}{HHH} TTHHHTH,\]
the red letters form a run of length $3$. (A run of length $1$ is still considered a run.)
If a fair coin is flipped two times, what is the expected number of runs? (If you're confused about how to count the number of runs, the example sequence above has $6$ runs.)
