Question 14
Let $x_{1}, \ldots, x_{100}$ be defined so that for each $i$, $x_{i}$ is a (uniformly) random integer between $1$ and $6$ inclusive. Find the expected number of integers in the set $\{x_{1}, x_{1}+x_{2}, \ldots, x_{1}+x_{2}+\ldots+x_{100}\}$ that are multiples of $6$.