An unbiased six-faced dice (faces 1-6) is rolled twice. The probability that the number appearing in

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Question

An unbiased six-faced dice (faces 1-6) is rolled twice. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is:

Accepted Answer

Correct Answer: (C) 7/18Concept -- Probability with Sample Space Counting: The total number of ordered pairs (first roll, second roll) = 6 × 6 = 36. We count favorable pairs where the second number is an integer multiple of the first. For each possible first roll f, the valid second rolls are multiples of f that are ≤6: f=1 → multiples: 1,2,3,4,5,6 (6 pairs). f=2 → multiples: 2,4,6 (3 pairs). f=3 → multiples: 3,6 (2 pairs). f=4 → multiples: 4 (1 pair). f=5 → multiples: 5 (1 pair). f=6 → multiples: 6 (1 pair). Total favorable = 6+3+2+1+1+1 = 14. Probability = 14/36 = 7/18. This is a standard example of counting with the 'multiple' relation, illustrating the use of systematic enumeration and reduction of fractions. The probability is less than 1/2 because larger first numbers have fewer multiples.

An unbiased six-faced dice (faces 1-6) is rolled twice. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is:

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An unbiased six-faced dice (faces 1-6) is rolled twice. The probability that the number appearing in the second roll is an integer multiple of the number appearing in the first roll is:

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