Brain Teasers & Mental Math
Roll two fair dice. What is the expected value of the LARGER of the two numbers?
Model answer
161/36 ≈ 4.47.
Fastest path: P(max ≤ k) = (k/6)², so P(max = k) = (k² − (k−1)²)/36 = (2k − 1)/36. That gives probabilities 1, 3, 5, 7, 9, 11 (over 36) for k = 1…6.
E(max) = Σ…
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