Solution
Max of Two Dice
Show the problem again
Roll two fair six-sided dice. What is the expected value of the larger of the two values? Express as a fraction.
Worked solution
The answer is 161/36 ≈ 4.47. P(max = k) = (2k − 1)/36, since the max equals k in the 2k − 1 outcomes where at least one die shows k and neither exceeds it. Then E[max] = Σ k(2k − 1)/36 = (2·91 − 21)/36 = 161/36.
Source: Standard dice-maximum exercise from introductory probability texts. Statement written for AxiomIQ.