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Q: How many elements are in the event space if you roll a sum of 12 with 2 dice?

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Three.

There are two elements in the event space. They are the rolls (6, 5) and (5, 6) .

There are 5 elements in the event space if you roll a sum of 8 with 2 dice; 2,6 & 6,2 & 3,4 & 4,3 & 4,4.

Two.

216

Only one is.

A sum of 9 with 2 dice can be achieved with 3+6, 4+5, 5+4, and 6+3, so there are 4 elements in the event space for a sum of 9. This corresponds to a probability of 4 in 36, or 1 in 9, or about 0.1111 for that result.

36, if they are standard dice.

11 outcomes if the dice are indistinguishable, 36 otherwise.

There are 36.

There are 64 = 1296 of them.

36

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