Multiple choice

A special die with numbers $1, -1, 2, -2, 0$ and $3$ is thrown thrice. What is the probability that the total is zero?

  1. $\displaystyle \frac{25}{216}$
  2. $\displaystyle \frac{1}{6}$
  3. $\displaystyle \frac{1}{9}$
  4. $\displaystyle \frac{1}{12}$
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A Correct answer
AI explanation

The total number of outcomes for throwing the die thrice is 6^3 = 216. To find the favorable outcomes where the sum is zero, we look at sets of three numbers that cancel out, such as one zero with a matching pair like (1, -1, 0) giving 12 permutations, two zeros with any number like (1, 0, 0) giving 6 permutations, and sets of three non-zeros summing to zero like (1, 2, -3) giving 6 permutations. Adding all permutations from valid sets like (1, -1, 0), (2, -2, 0), (1, 0, 0), (-1, 0, 0), (2, 0, 0), (-2, 0, 0), (3, 0, 0), (-3, 0, 0), (1, 2, -3), (-1, -2, 3), (1, -3, 2) and (-1, 3, -2) yields 25 total favorable outcomes. The probability is therefore 25 / 216.

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