GATE CS 2026 Set 2 Q.10: 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 ________

$\frac{3}{36}$

$\frac{13}{36}$

$\frac{15}{36}$

$\frac{19}{36}$

Official answer and solution

Official answer: C
From: Official GATE 2026 answer key

Solution

Count the number of ordered outcomes $(d_1, d_2) \in \{1,\dots,6\}^2$ whose sum is prime ( $2, 3, 5, 7,$ or $11$ ).

When a fair six-faced die is rolled twice, there are $6 \times 6 = 36$ equally likely outcomes. The possible sums range from $2$ to $12$ , and the prime sums in this range are $2, 3, 5, 7, 11$ :

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

Total favorable outcomes $= 1 + 2 + 4 + 6 + 2 = 15$ , giving probability $\frac{15}{36}$ .

Final answer

Option (C)

Common trap

Forgetting that $2$ is a prime number, which would give $14/36$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 10 of 65
Section: General Aptitude

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