GATE 2026 CS (CS2) – Question 10
An unbiased six-faced die 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 ________.
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Correct answer: (C) $\frac{15}{36}$
Explanation
When two fair dice are rolled, there are 36 equally likely outcomes. The possible prime sums are 2, 3, 5, 7, and 11. The number of outcomes giving these sums is 1, 2, 4, 6, and 2, respectively. Thus the total number of favorable outcomes is $1+2+4+6+2=15$. Hence, the required probability is $\frac{15}{36}$. Therefore, option (C) is correct.