9 fair coins are independently tossed in a row. Let $$X$$ 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 $$X$$ has the form $$\frac {a}{b}$$, where $$a$$ and $$b$$ are coprime integers. What is the value of $$a+b$$?

Details and assumptions

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

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