# When 3 dice are rolled, which number is least likely to be the sum.

justaguide | College Teacher | (Level 2) Distinguished Educator

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When 3 dice are rolled, the sum can be any of the numbers from 3 to 18. The sum is 3 when all the three dice show 1 and the sum is 18 when all the three dice show 6. In both of these cases, the is no other combination of numbers on the dice that results in that sum. This is unlike the case for any other number, for example the sum 5 can be obtained if the number on the dice is either {1, 1, 3} or {2, 2, 1}

The numbers least likely to be the sum when 3 dice are rolled are 3 and 18.

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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If you have 3 dice, each with faces 1-6, your sums will be between 3 (1+1+1) and 18 (6+6+6). Since you only have 3 dice, there is no other way to roll a sum of 3 or a sum of 18. The only way to roll a sum of 3 is with three ones. The only way to roll a sum of 18 is with three sixes. Therefore those would be the least likely sums to occur.

However that also happens with 4 (you can only roll a 2, 1, and 1 to get a sum of 4 if you roll all 3 dice). I would also say that is one that you won't get as often as others.

nisarg | Student, Grade 11 | (Level 1) Valedictorian

Posted on

Least likely is 3 and 18 because the only things that add up to those are 3 1's or 3 6's.