# If two dice are rolled what are the odds that the sum of the faces is 2, 3 or 12.

justaguide | Certified Educator

Each die has each faces with the numbers 1 to 6. When two dice are rolled there are 6*6 = 36 possible outcomes for the sum.

For the sum to be 2, only one possibility exists (1, 1)

For the sum to be 3, there are two possibilities (1, 2) and (2, 1)

For the sum to be 12, there is only one possibility (6, 6)

The total number of ways in which the sum of the faces when two dice are rolled is 2, 3 or 12 is 5. As there are 36 possible outcomes, the odds of this happening are 4/36 = 1/9.

The odds of the sum of the faces of two dices being 2, 3 or 12 is 1/9.

mathsworkmusic | Certified Educator

The odds of an event is not the same as the probability. The probability of rolling any of these combinations is 1/9 but the odds is (1/9)/(8/9) = 1:8

The odds of an event is the probability of it happening divided by the probability of it not happening.

The odds of getting dice that sum to 2,3 or 12 is 1:8