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Directions for Q. 19 & Q… (Class 10 Maths Basic 2023, Q19)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2023: question 19

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, 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

Directions for Q. 19 & Q. 20: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The probability that a leap year has 53 Sundays is .

Reason (R): The probability that a non-leap year has 53 Sundays is .

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

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Count the days left over after 52 complete weeks.

Hint 2

A leap year has 2 extra days and a non-leap year has 1.

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. A leap year has 52 weeks + 2 extra days. These 2 days can be any of 7 equally likely pairs, and 2 of them (Sat-Sun, Sun-Mon) contain a Sunday, so P . A is true.

  2. A non-leap year has 52 weeks + 1 extra day, so P(53 Sundays) . R is true, but it is about non-leap years and does not explain A, so option (B).

    1 mark

Answer: Option (B)

Where the marks are

  • Shows both A and R are true but R does not explain A (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 paper2023 board paper, set 430/6/1 (Basic): 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.