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Old 10-06-2016, 10:31 AM
chrisk chrisk is offline
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Join Date: Nov 2003
Location: Southern ontario
Posts: 6,564
I don't think I agree... though as with many probabilities problems, it may be that I'm missing something or am making an assumption that others aren't. Here's my reasoning:

I roll the 2 dice. To begin with, there are 36 different possibilities, (counting the red die and the green die separately.)

I observe, "Hey, there's a six here." That eliminated 25 possibilities, all the ones composed only of 1 through 5 on both dice, and leaves 11 possibilities left, out of which only one is double-sixes.

Now, for each of these eleven possibilities, I can pick a six and take it off the table. Since I can always do that, doing it doesn't change the original odds of rolling double sixes... the way the observation about having at least one six did. (That changed the odds, because there were many possible rolls in which I couldn't make that observation.)

Thus, even after I've taken that die and removed it from the table, the odds that I originally rolled double sixes is still 1 in 11.

The remaining die still on the table will be a 6 if-and-only-if I rolled double sixes. Thus, the odds that the die on the table is a 6 is also 1 in 11.

No, the dice don't communicate, and yes, the outcome of the dice is independent. But that observation of both dice together does change the answer, as does the process of "looking for" one six and selectively removing it from the table... assuming that I would announce my observation and remove one six every time I roll a result that has one or more sixes. That's the assumption.

Edited to add: If, on the other hand, we assume that I removed one die from the table at random, and it happened to be a die showing a six... then I think the answer of 1 in 6 is correct.
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Last edited by chrisk; 10-06-2016 at 10:35 AM.