Multiple choice

Two uniform dice marked $1$ to $6$ are thrown together. The probability that the sum is not a prime number is

  1. $\frac{1}{4}$
  2. $\frac{5}{12}$
  3. $\frac{7}{12}$
  4. $\frac{9}{12}$
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C Correct answer
Explanation

The total outcomes for two dice are 36. Sums that are prime are 2, 3, 5, 7, 11. Counting the pairs for these sums: (1,1), (1,2), (2,1), (1,4), (4,1), (2,3), (3,2), (1,6), (6,1), (2,5), (5,2), (3,4), (4,3), (5,6), (6,5). There are 15 prime sums, so 21 sums are not prime. The probability is 21/36 = 7/12.

AI explanation

When two dice are thrown, the total number of possible outcomes is 6 multiplied by 6, which equals 36. The sums that are prime numbers are 2, 3, 5, 7, and 11, which account for 15 possible combinations. Using the complementary probability rule, the probability that the sum is not prime is 36 minus 15, which is 21 favorable outcomes out of 36, simplifying to 7/12.

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