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

When two dice are tossed, each die shows 1 to 6, so the total number of possible results is 6 × 6 = 36. The totals can run from 2 up to 12.

The prime totals in that range are 2, 3, 5, 7 and 11. Now count how many ways each one happens: total 2 → 1 way (1+1); total 3 → 2 ways (1+2, 2+1); total 5 → 4 ways (1+4, 4+1, 2+3, 3+2); total 7 → 6 ways (1+6, 6+1, 2+5, 5+2, 3+4, 4+3); total 11 → 2 ways (5+6, 6+5).

Add them: 1 + 2 + 4 + 6 + 2 = 15 favourable results. So the probability = 15/36, and dividing top and bottom by 3 gives 5/12. Remember 1 is not prime and 9 is not prime (9 = 3 × 3), so those totals are left out.