Question

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Suppose we flip a fair coin n times. We say that the sequence is balanced when there are equal number of heads and tails. For example, if we flip the coin 10 times and the results areHTHHTHTTHH, then this sequence balanced 2 times, i.e. at position 2 and position 8 (after the second and eighth flips).

In terms of n, what is the expected number of times the sequence is balanced within n flips?

Answer 1

Performed tossing the coin for 1000 times for 1000 iterations and tried to capture the results.

The nature as observed in the above graph is very random for 1000 iterations of 1000 rolls and the count variable's bar plot says the nature is very random with max 33 times the ans is 8 Hence you cannot generalize ans in terms of n

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