Multiple choice

When a pair of six faced fair dice are thrown, the probability that the sum of the numbers on the two dice is greater than $7$, is

  1. $\cfrac { 1 }{ 3 } $
  2. $\cfrac { 5 }{ 12 } $
  3. $\cfrac { 1 }{ 2 } $
  4. $\cfrac { 1 }{ 4 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 36. Sum > 7: sums of 8, 9, 10, 11, 12. Outcomes: (2,6), (3,5), (4,4), (5,3), (6,2) [5]; (3,6), (4,5), (5,4), (6,3) [4]; (4,6), (5,5), (6,4) [3]; (5,6), (6,5) [2]; (6,6) [1]. Total = 5+4+3+2+1 = 15. Probability = 15/36 = 5/12.

AI explanation

The total number of outcomes for rolling a pair of dice is 36. The combinations that yield a sum greater than 7 are 15 in total: 5 outcomes for a sum of 8, 4 outcomes for 9, 3 outcomes for 10, 2 outcomes for 11, and 1 outcome for 12. The probability is therefore 15 divided by 36, which simplifies to 5/12.

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