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roll two fair dice until you get three consecutive numbers from smaller to larger regarding the sum of two dice outcomes. what can be the total probability of achieving that goal? i.e : 2 3 2 7 6 12 6 5 4 stop. 9th roll you have achieved. begining from 3th roll each roll whan can be the formula for calculating probability for each roll?

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Your example doesn’t match the description of the problem: you’ve ended with three consecutive numbers from largest to smallest, not from smallest to largest. – Brian M. Scott Dec 20 '12 at 10:29
Brian - Surely it doesn't matter lol. There are 11 outcomes of rolling 2 dice and "7" is the middle number, with 5 numbers on either side with equal probabilities. The probability of having 3 consecutive numbers from smallest to largest is the same as the probability of having 3 consecutive numbers from largest to smallest. – Adam Rubinson Dec 20 '12 at 13:36
@Adam: That’s obvious, and not the point of my question. The problem is that we don’t know whether the disagreement between description and example is simply a mistake, or whether the OP actually means that both orders are allowed, which does make a difference. – Brian M. Scott Dec 20 '12 at 17:59
if both orders are allowed, then surely the probability is double that of when only one order is allowed... – Adam Rubinson Dec 21 '12 at 11:48
@Adam: Plainly. But before spending much time thinking about the question, it would be nice to know whether the OP is sufficiently interested to clarify it. (By the way, it’s sheer accident that I saw either of your comments. You need to include @Brian if you want to be sure that I’ll see a comment.) – Brian M. Scott Dec 23 '12 at 22:19

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