293.Six Before Five
★★★conditional probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
Roll a fair 6-sided die until a 6 appears. Given that the first 6 occurs before the first 5, find the expected number of rolls.
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The unconditional answer would be 6 — but conditioning on "no 5 before the 6" penalizes long sequences. Work out the conditional distribution of the number of rolls.
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