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In a survey on holidays, 120… (Class 10 Maths 2024, Q38)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2024: question 38

Set in the CBSE Class 10 board exam of 2024, 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

In a survey on holidays, people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.

Observe the pie chart and answer the following questions:

  1. (i)

    If one person is selected at random, find the probability that he/she travelled by bus or ship.

    1 mark
  2. (ii)

    Which is most favourite mode of transport and how many people used it?

    1 mark
  3. (iii)

    (a) A person is selected at random. If the probability that he did not use train is , find the number of people who used train.

    2 marks

  4. OR

    (iii)

    (b) The probability that randomly selected person used aeroplane is . Find the revenue collected by air company at the rate of ₹ per person.

    2 marks

Figure in the paper: Pie chart of 120 people by mode of transport. Sectors in order: Ship 33°, Aeroplane (no angle printed), Train (no angle printed), Bus 36°, and Car 177°. The Car sector is at the bottom of the circle, and the Ship, Aeroplane and Train sectors lie in the upper-left and upper portion. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

In a pie chart, probability = sector angle ÷ 360°.

Hint 2

Number of people in a mode = (sector angle ÷ 360°) × 120, or probability × 120.

Hint 3

For (iii)(a), use P(E) = 1 − P(not E). Then multiply the probability by the total number of people.

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 angles of the bus and ship sectors together are out of . So P(bus or ship) .

    1 mark

  2. (ii) Car has the largest sector (), so car is the most favourite mode of transport.

    ½ mark

  3. Number of people who used car .

    ½ mark

  4. (iii)(a) P(used train) .

    1 mark

  5. Number of people who used train .

    1 mark

  6. (iii)(b) Number of people who used aeroplane .

    1 mark

  7. Revenue collected .

    1 mark

Answer: (i) 23/120; (ii) Car, 59 people; (iii)(a) 24 people; (iii)(b) ₹70,000

Where the marks are

  • (i) Gets P(bus or ship) (1 mark)
  • (ii) Identifies car as the most favourite mode (½ mark)
  • (ii) Finds that 59 people used car (½ mark)
  • (iii)(a) Finds P(train) using the complement (1 mark)
  • (iii)(a) Finds that 24 people used train (1 mark)
  • (iii)(b) Finds that 14 people used aeroplane (1 mark)
  • (iii)(b) Finds the revenue ₹70,000 (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 30/2/1 (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.