The hardness of the butter is proportional to the softness of the bread. 
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Game of Craps  AnswerThe number of rolls of the dice you can expect in a game of craps is 3.376. Here's the solution: The frequency (F) of each number (N) rolled is F(N) = (6  lN  7l) / 36. Of all 36 possibilities, the 12 which have an N of 2, 3, 7, 11, or 12 end on the first roll. For other values or N, the probability of ending on the next roll is P(N) = F(N) + F(7). So the expected number of rolls after the first roll for these values of N is 1 / P(N). For all possibilities, the expected number of rolls is


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