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Case Study 3. Computer-based… (Class 10 Maths 2023, Q38)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2023: question 38

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section E, question 38, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q38 · 4 marks · Case-basedCompetency-basedProbability

Case Study 3. Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on elementary and secondary schools of Assam and they were classified by the number of computers they had.

Number of Computers1–1011–2021–5051–100101 and more
Number of Schools25020029018080

One school is chosen at random. Then :

  1. (i)

    Find the probability that the school chosen at random has more than computers.

    1 mark
  2. (ii)

    (a) Find the probability that the school chosen at random has or fewer computers.

    2 marks

  3. OR

    (ii)

    (b) Find the probability that the school chosen at random has no more than computers.

    2 marks
  4. (iii)

    Find the probability that the school chosen at random has or less than computers.

    1 mark

Figure in the paper: A photograph of a computer lab with rows of desks, each with a monitor and a black chair, and a projector screen on the wall at the back. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

Probability = number of favourable schools ÷ total number of schools (1000).

Hint 2

Decide which columns of the table fit each condition, for example, 'more than 100' means the '101 and more' column.

Hint 3

'50 or fewer' and 'no more than 20' mean you add up every column up to that number.

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. (i) Schools with more than 100 computers (101 and more) = 80, out of 1000 schools in total.
    P(more than 100) .

    1 mark

  2. (ii)(a) Schools with 50 or fewer computers come from the classes 1–10, 11–20 and 21–50: .

    1 mark

  3. P(50 or fewer) .

    1 mark

  4. (ii)(b) Schools with no more than 20 computers come from the classes 1–10 and 11–20: .

    1 mark

  5. P(no more than 20) .

    1 mark

  6. (iii) Schools with 10 or fewer computers (class 1–10) = 250.
    P .

    1 mark

Answer: (i) 0.08; (ii)(a) 0.74; (ii)(b) 0.45; (iii) 0.25

Where the marks are

  • (i) 80/1000 = 0.08 (1 mark)
  • (ii)(a) Counts 250 + 200 + 290 = 740 (1 mark); probability 0.74 (1 mark)
  • (ii)(b) Counts 250 + 200 = 450 (1 mark); probability 0.45 (1 mark)
  • (iii) 250/1000 = 0.25 (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 30/2/1 (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.