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A box contains 90 discs which… (Class 10 Maths 2024, Q27b)

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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(b)

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

Q27(b) · 3 marks · Short answerProbability

A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a :

  1. (i)

    2-digit number less than 40.

    1 mark
  2. (ii)

    number divisible by 5 and greater than 50.

    1 mark
  3. (iii)

    a perfect square number.

    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

Remember 2-digit numbers start at 10, and 50 itself is not greater than 50.

Hint 2

List the favourable numbers in each case and divide by 90.

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. Total number of outcomes = 90.

  2. (i) 2-digit numbers less than 40 are 10, 11, ..., 39: 30 numbers.

    1 mark

  3. (ii) Numbers divisible by 5 and greater than 50: 55, 60, 65, 70, 75, 80, 85, 90 — 8 numbers.

    1 mark

  4. (iii) Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81 — 9 numbers.

    1 mark

Answer: (i) 1/3; (ii) 4/45; (iii) 1/10

Where the marks are

  • P(2-digit number < 40) = 30/90 = 1/3 (1 mark)
  • P(divisible by 5 and > 50) = 8/90 = 4/45 (1 mark)
  • P(perfect square) = 9/90 = 1/10 (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.