Head-Tail Coin Tosses

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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