Head-Tail Coin Tosses

Discrete Mathematics 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.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.