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Counting & ProbabilityChallengeExpected Value, Linearity & Advanced Probability

Expected Value, Linearity & Advanced Probability · Challenge problem

A fair six-sided die is rolled 2020 times. Call roll number kk (for 2≤k≤202\le k\le20) a step up if it shows a strictly larger number than roll k−1k-1. What is the expected number of step ups? Express your answer as a common fraction.