The Puzzle of Probability Itself

[Wolrab]

I've been on this forum long enough to know it is either a six or it is not, so 50/50. Or the odds that Sally ever even exists are so high as to be incalculable. Therefore God.....unless Sally is the Antichrist then it would most assuredly come up as a six as well as a hypothetical third die.

Do I have to teach you people everything?!

 

[Dave Rogers]

The original problem doesn't state what Sally knows. That's why it's ambiguous. But I don't think the problem is about Sally. Stripped down, I think its intent is to ask, if two dice are rolled, and one of them is a 6, what is the probability that the other die is a 6. As I said, the problem appears to be a variation on a problem that is in every elementary probability text: You meet a man on the street who tells you he has two children, one of whom is a girl. What is the probability that his other child is a girl?

Damn, yes, you're right. I hate being caught out by Bayesian statistics. As long as there's no way to distinguish between the two dice a priori, then the odds are 1/11.

Correct me if I'm wrong, but if I then ask Sally, "Are the two dice the same colour," and she says no, don't the odds become 1/6? That would strike me as exactly the sort of thing Marplots was talking about in the OP.

Dave

 

[jt512]

Damn, yes, you're right. I hate being caught out by Bayesian statistics. As long as there's no way to distinguish between the two dice a priori, then the odds are 1/11.

Correct me if I'm wrong, but if I then ask Sally, "Are the two dice the same colour," and she says no, don't the odds become 1/6? That would strike me as exactly the sort of thing Marplots was talking about in the OP.

Whether the dice are distinguishable or not does not per se affect the probability. For instance, knowing that one die is blue and the other red, and that one of them is a "six," the probability of the other die being "six" would still be 1/11. On the other hand, if we knew that one die was blue and the other die red, and that the blue was a "six," then the probability that the other die was a "six" would be 1/6.

 

[Dave Rogers]

Whether the dice are distinguishable or not does not per se affect the probability. For instance, knowing that one die is blue and the other red, and that one of them is a "six," the probability of the other die being "six" would still be 1/11. On the other hand, if we knew that one die was blue and the other die red, and that the blue was a "six," then the probability that the other die was a "six" would be 1/6.

Yes, but the original problem stated that Sally showed that one of the dice was a six, so we now can assume that we know its colour. If we then are told that the other die is a different colour, then we can eliminate five possible solutions and return to 1/6 probability that the other dice is a 6, can't we?

Dave