Multiple choice

If three dice are rolled once, the number of ways of getting atleast one prime number on the dice is____

  1. 189

  2. 169

  3. 179

  4. 159
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A Correct answer
Explanation

Total outcomes for 3 dice = 6^3 = 216. Outcomes with no prime numbers (only 1, 4, 6) = 3^3 = 27. Outcomes with at least one prime = 216 - 27 = 189.

AI explanation

When three dice are rolled, the total number of possible outcomes is 6^3 = 216. The prime numbers on a die are 2, 3, and 5, making 3 options, while the non-prime numbers (1, 4, 6) also make 3 options. Using the complement method, the number of outcomes with no prime numbers is 3^3 = 27. Therefore, the number of outcomes with at least one prime number is 216 - 27 = 189.

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