easy Probability

Maximal Dice

A release-checked easy problem for training Dice.

Question

$k \geq 1$ fair n-sided die with the values $1-n$ on the sides are rolled. Find the probability that the maximum value among the $k$ dice is $1 \leq r \leq n$. Compute this with $k = 3, r = 4,$ and $n = 6$.

Practice focus

This Probability problem is tagged Dice. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.