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?

For your second answer, where you list the repetitions, there are 12 cases where you report seeing a 2 (6 on the first list and 6 on the second), two of which are wins, so wouldn't the probability be 2/12 rather than 2/11?  This would agree with my answer of 1/6 via slightly different reasoning. 

Posted by tomarken on 2016-04-20 14:06:57