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Three unbiased coins are tossed… (Class 10 Maths 2024, Q30)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 30

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, 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. (i)

    at least one head.

    1 mark
  2. (ii)

    exactly one tail.

    1 mark
  3. (iii)

    two heads and one tail.

    1 mark

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

List all possible outcomes of tossing three coins — there are 8.

Hint 2

For 'at least one head', it is easier to remove the outcome with no head.

Hint 3

Exactly one tail means the other two coins show heads.

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, THH, HTT, THT, TTH, TTT}; total outcomes = 8.
    (i) At least one head: all except TTT, i.e. 7 outcomes. P

    1 mark

  2. (ii) Exactly one tail: HHT, HTH, THH — 3 outcomes. P

    1 mark

  3. (iii) Two heads and one tail: HHT, HTH, THH — 3 outcomes. P

    1 mark

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

Where the marks are

  • (i) P(at least one head) = 7/8 (1 mark)
  • (ii) P(exactly one tail) = 3/8 (1 mark)
  • (iii) P(two heads and one tail) = 3/8 (1 mark)

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 paper2024 board paper, set 30/5/1 (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.