Average of the lowest of three dice

Three fair six-sided dice are rolled. What is the expected value of the smallest of the three results?

$\tfrac{49}{24}$. Use the tail-sum formula: $\mathbb{P}(\min\ge k)=\left(\tfrac{7-k}{6}\right)^3$, so $\mathbb{E}[\min]=\sum_{k=1}^{6}\left(\tfrac{7-k}{6}\right)^3=\tfrac{216+125+64+27+8+1}{216}=\tfrac{441}{216}=\tfrac{49}{24}$.