Two fair 6-sided dice are rolled simultaneously. What is the probability that the sum of the numbers rolled is a prime number?

Answer and explanation

Correct answer: D. 5/12

Sum = 2: (1,1) -> 1
Sum = 3: (1,2), (2,1) -> 2
Sum = 5: (1,4), (2,3), (3,2), (4,1) -> 4
Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) -> 6
Sum = 11: (5,6), (6,5) -> 2.
  1. Step 1: Possible sums range from 2 to 12. Total outcomes = 6 * 6 = 36.
  2. Step 2: Prime sums are 2, 3, 5, 7, 11.
  3. Step 3: Count outcomes for each prime sum:
  4. Step 4: Total favorable outcomes = 1 + 2 + 4 + 6 + 2 = 15.
  5. Step 5: Probability = 15 / 36 = 5 / 12.
Answer
5/12.
Why not the others: 7/18 computes 14/36 (omitting sum = 2); 1/2 assumes 18 outcomes; 1/3 computes 12/36.

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