Computer Sciences > GATE 2026 SET-1 > Probability
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 number appearing in the second roll is an
integer multiple of the number appearing in the first roll is __________
Correct : c
The correct answer is Option C: 7/18.
Total possible outcomes when a die is rolled twice = 6 × 6 = 36.
We need to count pairs (a, b) where b is an integer multiple of a:
• First roll = 1: multiples in {1,2,3,4,5,6} → {1,2,3,4,5,6} → 6 pairs
• First roll = 2: multiples → {2,4,6} → 3 pairs
• First roll = 3: multiples → {3,6} → 2 pairs
• First roll = 4: multiples → {4} → 1 pair
• First roll = 5: multiples → {5} → 1 pair
• First roll = 6: multiples → {6} → 1 pair
Total favorable outcomes = 6 + 3 + 2 + 1 + 1 + 1 = 14
P = 14/36 = 7/18
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