Random Variables · Challenge problem

A shop's visitors are of two kinds. With probability $\dfrac13$ a visitor only browses and buys nothing; with probability $\dfrac23$ the visitor buys a number of items equal to the roll of a fair six-sided die. Let $X$ be the number of items a random visitor buys. Find $\mathrm{Var}(X)$. Express your answer as a common fraction.