GATE CS 2026 Set 2 Q10 — General Aptitude

When an unbiased six-faced die is rolled twice, the total number of possible outcomes in the sample space is:

The sum of the numbers on the two faces can range from $2$ (minimum, $1+1$) to $12$ (maximum, $6+6$). The prime numbers in this range are $2, 3, 5, 7,$ and $11$.

Let us list the favorable outcomes for each prime sum:

• Sum = 2: $(1, 1)$ — $1$ outcome
• Sum = 3: $(1, 2), (2, 1)$ — $2$ outcomes
• Sum = 5: $(1, 4), (2, 3), (3, 2), (4, 1)$ — $4$ outcomes
• Sum = 7: $(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)$ — $6$ outcomes
• Sum = 11: $(5, 6), (6, 5)$ — $2$ outcomes

Total number of favorable outcomes = $1 + 2 + 4 + 6 + 2 = 15$.

Therefore, the probability that the sum is a prime number is:

Thus, the correct option is C.