Computer Sciences > GATE 2026 SET-2 > Quantitative Aptitude
An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice in succession and the number on the top face is recorded each time. The probability that the sum of the two recorded numbers is a prime number is ______.
Correct : c
A dice is rolled twice, so the total number of equally likely outcomes is 6 × 6 = 36. The sum of two dice can range from 2 to 12. Among these, the prime numbers are 2, 3, 5, 7, and 11. Note that 4, 6, 8, 9, 10 and 12 are not prime, and sums less than 2 or greater than 12 are not possible.
Now counting all ordered pairs (first roll, second roll) that give a prime sum:
Sum = 2 (prime): (1,1) → 1 way
Sum = 3 (prime): (1,2), (2,1) → 2 ways
Sum = 5 (prime): (1,4), (4,1), (2,3), (3,2) → 4 ways
Sum = 7 (prime): (1,6), (6,1), (2,5), (5,2), (3,4), (4,3) → 6 ways
Sum = 11 (prime): (5,6), (6,5) → 2 ways
Total favourable outcomes = 1 + 2 + 4 + 6 + 2 = 15
Probability = 15/36
Correct answer: C — 15/36 ✓
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