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Some students were asked… (Class 10 Maths Basic 2023, Q38)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2023: question 38

Set in the CBSE Class 10 board exam of 2023, paper 430/5/1, 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

Some students were asked to list their favourite colour. The measure of each colour is shown by the central angle of a pie chart given below.

Study the pie chart and answer the following questions:

  1. (i)

    If a student is chosen at random, then find the probability of his/her favourite colour being white?

    1 mark
  2. (ii)

    What is the probability of his/her favourite colour being blue or green?

    1 mark
  3. (iii)(a)

    If 15 students liked the colour yellow, how many students participated in the survey?

    2 marks

  4. OR

    (iii)(b)

    What is the probability of the favourite colour being red or blue?

    2 marks

Figure in the paper: A pie chart divided into five sectors with central angles: Blue , Red , Yellow , White , Green . Blue and Green are at the upper part, Red at the upper right, Yellow at the lower right, and White at the lower left. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/5/1.

Hints

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

Hint 1

The fraction of students liking a colour equals its central angle divided by 360°.

Hint 2

For 'or', add the angles of both colours before dividing by 360°.

Hint 3

Yellow's 90° is a quarter of the circle, so 15 students form a quarter of the total.

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) The whole circle (360°) represents all students. P(white) .

    1 mark

  2. (ii) P(blue or green) .

    1 mark

  3. (iii)(a) Let the total number of students be . Yellow's share , so .

    1½ marks

  4. (iii)(a) , so 60 students took part in the survey.

    ½ mark

  5. (iii)(b) P(red or blue)

    1 mark

  6. (iii)(b) .

    1 mark

Answer: (i) 1/3; (ii) 1/3; (iii)(a) 60 students; (iii)(b) 1/4

Where the marks are

  • (i) P(white) = 120/360 = 1/3 (1 mark)
  • (ii) P(blue or green) = 120/360 = 1/3 (1 mark)
  • (iii)(a) Sets up (1½ marks)
  • (iii)(a) Gets 60 students (½ mark)
  • (iii)(b) Writes (30+60)/360 (1 mark)
  • (iii)(b) Simplifies to 1/4 (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 430/5/1 (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.