Multiple choice

Two dice are thrown together what is the probability that the sum of the number on the two face is divisible by 4 or 6?

  1. $\dfrac{1}{18}$
  2. $\dfrac{1}{9}$
  3. $\dfrac{7}{18}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total outcomes = 36. Sums divisible by 4: 4, 8, 12 (3, 5, 1 outcomes = 9). Sums divisible by 6: 6, 12 (5, 1 outcomes = 6). Sum 12 is counted twice. Total favorable = 9 + 6 - 1 = 14. Probability = 14/36 = 7/18.

AI explanation

When two dice are thrown, the total number of possible outcomes is 36. The sums that are divisible by 4 or 6 are 4, 6, 8, and 12; counting their specific combinations (3,1), (2,2), (1,3), (5,1), (4,2), (3,3), (2,4), (1,5), (6,2), (5,3), (4,4), (3,5), (2,6), and (6,6) gives 14 favorable outcomes. Using the addition rule for the combined event, the probability is 14 divided by 36. This simplifies to 7 divided by 18.

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