Multiple choice

Three dice are rolled simultaneously. The probability of getting the total sum of more than $5$ is

  1. $\dfrac{5}{54}$
  2. $\dfrac{67}{72}$
  3. $\dfrac{103}{108}$
  4. $\dfrac{53}{54}$
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C Correct answer
Explanation

Total outcomes for three dice = 6^3 = 216. The sum is 5 or less for combinations: (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,1,3), (1,3,1), (3,1,1), (1,2,2), (2,1,2), (2,2,1). There are 10 such outcomes. Probability of sum <= 5 is 10/216 = 5/108. Probability of sum > 5 is 1 - 5/108 = 103/108.

AI explanation

The total number of outcomes when rolling three dice is 6 x 6 x 6 = 216. To find the probability of getting a sum greater than 5, it is easier to calculate the complementary probability of getting a sum of 3, 4, or 5, which occurs in 1 + 3 + 6 = 10 ways. The probability of getting a sum of 5 or less is 10/216 = 5/108, so the probability of getting a sum greater than 5 is 1 - 5/108 = 103/108.

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