easy Probability

Tricky Die

A release-checked easy problem for training Combinations and Permutations, Dice.

Question

You have a 6-sided die before you with the values $1-6$ on the sides. The $6$ sides $1-6$, respectively, have probabilities $1/6, 1/6, 1/4 - x, 1/4 - 2x, 1/6,$ and $3x$ of appearing. Find the value of $x$ that minimizes the probability of obtaining a sum of $7$ when rolling the die twice.

Practice focus

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