Multiple choice

When two dice are thrown simultaneously, the probability that the sum of the two numbers that turn up is less than $11$ is:

  1. $\dfrac{11}{12}$
  2. $\dfrac{1}{12}$
  3. $\dfrac{2}{12}$
  4. $\dfrac{1}{8}$
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A Correct answer
Explanation

Total outcomes = 36. Sums >= 11 are (5,6), (6,5), (6,6), which are 3 outcomes. Sums < 11 are 36 - 3 = 33. Probability = 33/36 = 11/12.

AI explanation

When two dice are thrown, the total number of outcomes in the sample space is 36. The sum being 11 or more means the sum must be exactly 11 or exactly 12; the favourable pairs for this are (5,6), (6,5), and (6,6), totalling 3 outcomes. Using the complementary event rule, the probability of the sum being less than 11 is 1 minus the probability of it being 11 or more, calculated as 1 minus 3/36. This simplifies to 1 minus 1/12, resulting in a probability of 11/12.

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