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Could you please repeat that? (Posted on 2016-04-20) Difficulty: 3 of 5

At a craps table, I have a wager with the house that the shooter will make 4 'the hard way' i.e. {2,2}, at odds of 7:1 (with such bets, it doesn't matter what the shooter himself wants to score).

The shooter, an old man, tosses the dice. Unfortunately he is short-sighted, and can't see what he rolled, so he asks me, 'Can you see a 2 down there?'

To tell the truth, I am a bit near-sighted myself, and a touch hard of hearing, so I answer 'Could you please repeat that?' The old man says, ''What do you see down there? ' and I duly reply, 'I can see a 2, but I'm not sure what the other is'

What is the probability that I won my wager?

What would have been the probability, had I answered the shooter's original question?

See The Solution Submitted by broll    
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Solution Maybe the solution? | Comment 1 of 4
Not 100% sure this is correct but:

An answer "Yes" to the question "Can you see a 2 down there?" allows for 11 possible rolls (only one of which is 2,2 of course) so the probability would've been 1/11 if you had answered the original question.

On the other hand, "I can see a 2, but I'm not sure what the other is" clearly distinguishes one die as "the one you can see" from "the other one."  This allows only 6 possible rolls, so the probability is 1/6.  

  Posted by tomarken on 2016-04-20 10:00:23
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