Multiple choice

Two fair dice are thrown. What is the probability that the two scores do not add to $5$?

  1. $\dfrac{7}{9}$
  2. $\dfrac{5}{9}$
  3. $\dfrac{8}{9}$
  4. $\dfrac{1}{9}$
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C Correct answer
Explanation

Total outcomes for two dice = 36. Sum of 5 occurs for (1,4), (4,1), (2,3), (3,2) = 4 outcomes. Probability of sum 5 = 4/36 = 1/9. Probability of not sum 5 = 1 - 1/9 = 8/9.

AI explanation

When two fair dice are thrown, the total number of possible outcomes is 6 times 6 = 36. The combinations that give a sum of 5 are (1,4), (2,3), (3,2), and (4,1), meaning there are 4 ways to get a sum of 5. Using the complementary event rule, the probability of not getting a sum of 5 is 1 minus (4/36), which equals 32/36 or 8/9.

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