Two Dice Throw

Using probability theory, calculate the probability of getting totals of 2,3,4 .. 12 when throwing two six-sided dice.

Confirm your answer using the numerical simulation below. Consider the problem carefully, the answer might not be as simple as it first appears.

Throws Dice 1 Dice 2

. . .

Throws	Dice 1	Dice 2
.	.	.

Dice 1

1 2 3 4 5 6

Count . . . . . .

Count Percent . . . . . .

Dice 1
	1	2	3	4	5	6
Count	.	.	.	.	.	.
Count Percent	.	.	.	.	.	.

Dice 2

1 2 3 4 5 6

Count . . . . . .

Count Percent . . . . . .

Dice 2
	1	2	3	4	5	6
Count	.	.	.	.	.	.
Count Percent	.	.	.	.	.	.

Dice 1 + Dice 2

2 3 4 5 6 7 8 9 10 11 12

Count . . . . . . . . . . .

Count Percent . . . . . . . . . . .

Dice 1 + Dice 2
	2	3	4	5	6	7	8	9	10	11	12
Count	.	.	.	.	.	.	.	.	.	.	.
Count Percent	.	.	.	.	.	.	.	.	.	.	.

Analytical (calculation of probability using theory) and numerical (calculation of probability experimentally using dice, computers) methods can be used to confirm each other. If both methods agree, you can have higher confidence that the answer is correct (however, both methods might still be in error).

If both methods give different results, obviously one or both methods are wrong.