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Two dice of different colours… (Class 10 Maths 2026, Q31)

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

CBSE Class 10 Mathematics Standard 2026: question 31

Set in the CBSE Class 10 board exam of 2026, paper 30/1/1, 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 of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :

  1. (i)

    same number appears on both the dice?

    0 marks
  2. (ii)

    different number appears on both the dice?

    0 marks

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

Hints

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

Hint 1

Each die has 6 faces, so the number of ordered pairs is 6 × 6.

Hint 2

Count the 'doublets' like (2,2).

Hint 3

Different numbers is the complementary event of same number.

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. Write (first die, second die). All possible outcomes:

    (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
    (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
    (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
    (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
    (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
    (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

    Total number of outcomes = 36.

    1 mark

  2. (i) Outcomes with the same number on both dice: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), so 6 outcomes.

    P(same number)

    1 mark

  3. (ii) "Different numbers" is the complement of "same number".

    P(different numbers) (that is, )

    1 mark

Answer: 36 outcomes; (i) ; (ii)

Where the marks are

  • Lists all 36 outcomes correctly (1 mark)
  • (i) Finds P(same number) = 6/36 = 1/6 (1 mark)
  • (ii) Finds P(different numbers) = 5/6 (1 mark)

Revise the chapter

  • Chapter: Probability (notes, formulas, where marks are lost and every past question)
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 30/1/1 (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.