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Two dice are thrown at the same… (Class 10 Maths 2026, Q31)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 31

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerProbability

Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

List all ordered pairs (a, b) with a, b from 1 to 6.

Hint 2

For difference 3, count both (a, b) and (b, a), e.g. (1,4) and (4,1).

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. Total number of outcomes when two dice are thrown

    ½ mark

  2. (i) Favourable outcomes for sum 5: (1,4), (4,1), (2,3), (3,2) → 4.

    1 mark

  3. (ii) Favourable outcomes for difference 3: (1,4), (4,1), (2,5), (5,2), (3,6), (6,3) → 6.

    1½ marks

Answer: (i) ; (ii)

Where the marks are

  • Total outcomes = 36 (½ mark)
  • Lists 4 outcomes and gets (1 mark)
  • Lists 6 outcomes and gets (1½ marks)

Revise the chapter

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/2/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.