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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
TTHHHTTHHHTH,


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.)

 
 Oct 19, 2024

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