Question 43

Mathematics Probability Hard

Two fair dice are rolled. What is the probability that the total score is a prime number?

(A) <span class="math-tex">\(\dfrac{1}{6}\)</span>
(B) <span class="math-tex">\(\dfrac{5}{12}\)</span>
(C) <span class="math-tex">\(\dfrac{1}{2}\)</span>
(D) <span class="math-tex">\(\dfrac{7}{9}\)</span>
✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The possible prime totals are 2, 3, 5, 7 and 11.

  • 2: (1,1), 1 way
  • 3: 2 ways
  • 5: 4 ways
  • 7: 6 ways
  • 11: 2 ways

Total = 15 favourable outcomes out of 36.

Probability = \(\frac{15}{36} = \frac{5}{12}\)

Answer: (B) \(\frac{5}{12}\)

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