# In arup’s game of dice 3, you roll a fair pair of six-sided dice and record the total. if this total is 3, 5 or 12, you win. if it’s a 2 or 11, you lose. in all other cases, you roll the pair of dice

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In arup’s game of dice 3, you roll a fair pair of six-sided dice and record the total. if this total is 3, 5 or 12, you win. if it’s a 2 or 11, you lose. in all other cases, you roll the pair of dice again. if the sum of this second roll equals or exceeds the sum of your first roll, you win! otherwise you lose. (for example, if you roll a 6 followed by a 6, you win, but if you roll a 10 followed by a 9, you lose.) what is the probability of winning arup’s game of dice?

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