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

Given data

• Sums possible: 2 to 12 (36 equally likely outcomes).
• Prime sums: 2, 3, 5, 7, 11.

Concept/ApproachCount outcomes for each prime sum using standard dice-sum counts.

Step-by-step calculationSum 2: 1 way; 3: 2 ways; 5: 4 ways; 7: 6 ways; 11: 2 waysTotal favourable = 1 + 2 + 4 + 6 + 2 = 15Probability = 15/36 = 5/12

Verification/AlternativeNon-prime sums (4,6,8,9,10,12) account for 21 outcomes; 36 − 21 = 15.

Common pitfallsIncluding 1 or 13 as prime sums (not possible with two dice).

Final Answer5/12