Multiple choice

Two fair dice are rolled. Then, the probability of getting a composite number as the sum of face values is equal to

  1. $\cfrac { 7 }{ 12 } $
  2. $\cfrac { 5 }{ 12 } $
  3. $\cfrac { 1 }{ 12 } $
  4. $\cfrac { 3 }{ 4 } $
  5. $\cfrac { 2 }{ 3 } $
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A Correct answer
Explanation

Sums of two dice range from 2 to 12. Composite sums are 4, 6, 8, 9, 10, 12. Frequencies: 4(3), 6(5), 8(5), 9(4), 10(3), 12(1). Total = 3+5+5+4+3+1 = 21. Probability = 21/36 = 7/12.

AI explanation

When two dice are rolled, the 36 possible outcomes yield composite sums of 4, 6, 8, 9, 10, and 12. The total number of ways to get these sums is 3 for 4, 5 for 6, 5 for 8, 4 for 9, 3 for 10, and 1 for 12, adding up to 21 favorable outcomes. Using the classical probability formula, we divide 21 by 36. This simplifies to 7/12.

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