GATE CS 2026 Set 2 — Question 10
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Engineering Mathematics → Probability & Statistics → Elementary Statistics & Probability
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Question
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 answer
(C) (15)/(36)
Solution
Total number of outcomes when rolling two dice = .The possible sums range from to . The prime numbers in this range are 2, 3, 5, 7, 11.Let's 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
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