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Assertion (A) : Two coins are… (Class 12 Maths 2023, Q19)

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MathsCBSE Class 12 · Board exam 2023, set 65/5/1 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics 2023: question 19

Set in the CBSE Class 12 board exam of 2023, paper 65/5/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedProbability

Assertion (A) : Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is .

Reason (R) : Let E and F be two events with a random experiment, then .

  1. (A)Both (A) and (R) are true and (R) is the correct explanation of (A).
  2. (B)Both (A) and (R) are true, but (R) is not the correct explanation of (A).
  3. (C)(A) is true and (R) is false.
  4. (D)(A) is false, but (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/5/1.

Hints

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

Hint 1

List the sample space of two coins.

Hint 2

Apply .

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. E = at least one head = {HH,HT,TH}, P(E)=3/4; F = two heads, .

  2. ; A is true, R is the definition used, so R explains A.

    1 mark

Answer: option (A)

Where the marks are

  • Uses conditional probability to verify 1/3 (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 paper2023 board paper, set 65/5/1: 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.