Head-Tail Coin Tosses

Probability Level 5

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.