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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 14.1 Probability — A Theoretical Approach
Two dice are rolled together. The probability that the sum of the numbers obtained is divisible by 6, is :
  1. A $\frac{1}{6}$
  2. B $\frac{11}{36}$
  3. C $\frac{1}{12}$
  4. D $\frac{1}{4}$
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Model Answer

Option (A) $\dfrac{1}{6}$

Total outcomes = 36. Favourable outcomes (sum divisible by 6, i.e., sum = 6 or 12): (1,5),(2,4),(3,3),(4,2),(5,1),(6,6) → 6 outcomes. P = 6/36 = 1/6.

Explanation

Sums divisible by 6 from two dice can be 6 or 12 only (sum ranges from 2–12). List all pairs giving sum 6 (five pairs) and sum 12 (one pair) = 6 favourable outcomes out of 36. Students often miss (6,6) for sum 12 or miscount pairs for sum 6. Source: Chapter 14, Section 14.1

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