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Three unbiased coins are tossed… (Class 10 Maths 2025, Q30)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 30

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerProbability

Three unbiased coins are tossed simultaneously. Find the probability of getting :

  1. (a)

    exactly two tails

    1 mark
  2. (b)

    at least one head

    1 mark
  3. (c)

    at most two heads

    1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

List all 8 outcomes of tossing three coins.

Hint 2

'At least one head' excludes only TTT. 'At most two heads' excludes only HHH.

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. Sample space: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, so there are 8 equally likely outcomes.

  2. (a) Exactly two tails: HTT, THT, TTH, which is 3 outcomes.

    1 mark

  3. (b) At least one head: every outcome except TTT, which is 7 outcomes.

    1 mark

  4. (c) At most two heads: every outcome except HHH, which is 7 outcomes.

    1 mark

Answer: (a) ; (b) ; (c)

Where the marks are

  • (a) P(exactly two tails) = (1 mark)
  • (b) P(at least one head) = (1 mark)
  • (c) P(at most two heads) = (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 paper2025 board paper, set 30/3/1 (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.