The Gambler’s Puzzle
I was a gambler myself; I realized it at that moment. My arms and legs were trembling and my head throbbed. It was, of course, a rare happening for zero to come up three times out of some ten or so; but there was nothing particularly astonishing about it. I had myself seen zero turn up three times running two days before, and on that occasion one of the players, zealously recording all the coups on a piece of paper, had remarked aloud that no earlier than the previous day that same zero had come out exactly once in twenty four hours.
The probability of obtaining a zero on a (fair) Roulette wheel of the European variety is 1/37. Assuming that such a wheel is spun exactly 370 times in a day, determine the probability of obtaining at most one zero in twenty four hours as described in the quotation. Give your answer to three significant figures.
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