Head-Tail Coin Tosses

9 fair coins are independently tossed in a row. Let XX be the random variable denoting the number of instances in which a Head is immediately followed by a Tail during these 9 tosses. The variance of XX has the form ab\frac {a}{b}, where aa and bb are coprime integers. What is the value of a+ba+b?

Details and assumptions

Note: If we have 5 coins which are tossed as HTTHT\underline{HT}T\underline{HT}, there are 2 instances in which a Head is immediately followed by a Tail; they have been underlined.

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