Multiple choice

Two dice of different colours are thrown at a time. The probability that the sum is either $7$ or $11$ is

  1. $\dfrac{7}{36}$
  2. $\dfrac{2}{9}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{5}{9}$
  5. $\dfrac{6}{7}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 36. Sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Sum 11: (5,6), (6,5) = 2 outcomes. Total favorable = 8. Probability = 8/36 = 2/9.

AI explanation

The total number of possible outcomes when throwing two dice is 36. The 6 favorable outcomes for a sum of 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1), while the 2 favorable outcomes for a sum of 11 are (5, 6) and (6, 5). Using the addition theorem of probability, the combined number of successful outcomes is 8. The required probability is therefore 8/36, which simplifies to 2/9.

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