Multiple choice

Three fair dice are thrown. The probability of getting a sum $6$ or less on the three dice is

  1. $\dfrac {7 }{12}$
  2. $\dfrac {5 }{ 54}$
  3. $\dfrac {19 }{ 216}$
  4. $\dfrac {11 }{ 108}$
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

When three fair dice are rolled, the total number of possible outcomes is 6^3 = 216. The combinations of numbers on the three dice that give a sum of 6 or less are limited to sums of 3, 4, 5, and 6. Counting the permutations, there is 1 outcome for a sum of 3, 3 outcomes for a sum of 4, 6 outcomes for a sum of 5, and 10 outcomes for a sum of 6. The total number of favorable outcomes is 1 + 3 + 6 + 10 = 20, making the probability 20 / 216, which simplifies to 5 / 54.