Multiple choice

Two dice are thrown together. Find the probability that the two digit number formed with the two numbers turning up is divisible by $3$.

  1. $\dfrac{1}{2}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{2}{3}$
  4. $\dfrac{1}{6}$
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B Correct answer
Explanation

There are 36 possible outcomes when throwing two dice. The two-digit numbers formed range from 11 to 66; those divisible by 3 are 12, 15, 21, 24, 33, 36, 42, 45, 51, 54, 66 (total 12). The probability is 12/36 = 1/3.

AI explanation

A two-digit number formed by two dice is divisible by 3 only if the sum of the numbers on the two dice is a multiple of 3. The possible sums are 3, 6, 9, and 12, which correspond to 2, 5, 4, and 1 outcomes respectively, giving 12 total favorable outcomes. Since the total number of outcomes when two dice are rolled is 36, the required probability is 12/36 = 1/3.

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