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Double 6 Puzzle

Why the difference?

In puzzle 1, the die under the table is a complete mystery, so it still has its usual chances: one chance in six of also being a 6. Seeing a 6 on a particular die doesn’t change the second die’s ordinary roll chances.

In puzzle 2, all you know is that somewhere in the pair at least one 6 has appeared. If you look at all 36 outcomes of a roll of 2 dice, you see there are 11 different outcomes in which there is at least one 6. Only one of those 11 outcomes is the double six.

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