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Three coins are tossed… (Class 10 Maths 2024, Q27a)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 27(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section C, question 27(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(a) · 3 marks · Short answerProbability

Three coins are tossed simultaneously. What is the probability of getting

  1. (i)

    at least one head ?

    1 mark
  2. (ii)

    exactly two tails ?

    1 mark
  3. (iii)

    at most one tail ?

    1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

List all 8 possible outcomes of tossing three coins.

Hint 2

'At most one tail' means zero tails or one tail; count those outcomes.

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. Outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT — total 8.

  2. (i) At least one head: all except TTT, so 7 outcomes.

    1 mark

  3. (ii) Exactly two tails: HTT, THT, TTH — 3 outcomes.

    1 mark

  4. (iii) At most one tail: HHH, HHT, HTH, THH — 4 outcomes.

    1 mark

Answer: (i) 7/8; (ii) 3/8; (iii) 1/2

Where the marks are

  • P(at least one head) = 7/8 (1 mark)
  • P(exactly two tails) = 3/8 (1 mark)
  • P(at most one tail) = 4/8 = 1/2 (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 paper2024 board paper, set 30/4/1 (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.