posted by Ichigo .
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 ab, 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 (HT)T(HT), there are 2 instances in which a Head is immediately followed by a Tail; they have been grouped.