367.The Cashier's Change
★★★random walksCh. 1 — Classical Probability and Combinatorics444+ Problems in Probability
38 people are waiting to see a tennis match with a entrance fee. 19 of them have only bills and 19 have only bills, in uniformly random order, and the cashier starts with no change. What is the probability the cashier can always make change (a payer always receives a bill back)?
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Track (number of s received) minus (number of s received) as the line progresses — it must never go negative. Same machinery as the ballot problem.
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