Probability of rolling 2 6 sided dice and getting a sum of 12

What is the probability of rolling 2 6 sided dice and getting a sum of 12?

What is the probability of rolling 2 6 sided dice and getting an even sum?
What is the probability of rolling 2 6 sided dice and getting a sum of less then 13?

Question posted by: Jesse G

Probability of rolling an even sum with two 6-sided dice

There are a total of 6 sides on each die, resulting in 6 x 6 = 36 possible combinations when rolling two dice. To find the probability of rolling an even sum, we must first identify the number of combinations that result in an even sum.

Even sums can be obtained by rolling (1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), and (6,6). There are 18 combinations that yield an even sum.

The probability of rolling an even sum is the number of favorable outcomes (18) divided by the total possible outcomes (36). So, the probability is 18/36, which can be reduced to 1/2 or 0.5.

As a percentage, this probability is 50% (0.5 x 100%).

  1. Probability of rolling a sum less than 13 with two 6-sided dice:

Since the highest possible sum when rolling two 6-sided dice is 12 (rolling a 6 on each die), every possible combination will result in a sum less than 13. Therefore, the probability of rolling a sum less than 13 is 100%, as every roll of two 6-sided dice will always be less than 13.

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