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Case Study – 2 A middle school… (Class 10 Maths 2023, Q37)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2023: question 37

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedProbability

Case Study – 2

A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival.

Making Purple : Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'.

Based on the above, answer the following questions :

  1. (i)

    List all possible outcomes of the game.

    1 mark
  2. (ii)

    Find the probability of 'Making Purple'.

    1 mark
  3. (iii)

    (a) For each win, a participant gets ₹ 10, but if he/she loses, he/she has to pay ₹ 5 to the school. If 99 participants played, calculate how much fund could the school have collected.

    2 marks

  4. OR

    (iii)

    (b) If the same amount of ₹ 5 has been decided for winning or losing the game, then how much fund had been collected by school ? (Number of participants = 99)

    2 marks

Figure in the paper: Spinner I: circle divided into three sections: Red (R) upper left, Green (G) upper right, and Yellow (Y) at the bottom; an arrow pointer at the centre points toward the Red section. Spinner II: circle divided into three sections: Red (R) upper left, Blue (B) upper right, and Green (G) at the bottom; an arrow pointer at the centre points to the right toward the Blue section. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Pair each colour of Spinner I with each colour of Spinner II — how many pairs do you get?

Hint 2

Blue appears only on Spinner II, so count the pairs that give Red with Blue.

Hint 3

Use the probability to estimate winners among 99 players; the school gains from losers and pays out to winners.

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) Spinner I shows R, G or Y; Spinner II shows R, B or G. All possible outcomes (first letter from Spinner I):
    RR, RB, RG, GR, GB, GG, YR, YB, YG — 9 equally likely outcomes.

    1 mark

  2. (ii) Purple needs one Red and one Blue. Only Spinner II has Blue, so the only favourable outcome is RB.

    1 mark

  3. (iii)(a) Expected number of winners

    ½ mark

  4. (iii)(a) Number of losers

    ½ mark

  5. (iii)(a) Fund collected = amount received from losers − amount paid to winners

    1 mark

  6. (iii)(b) As before, with : winners

    ½ mark

  7. (iii)(b) Losers

    ½ mark

  8. (iii)(b) Each winner gets ₹5 and each loser pays ₹5:
    Fund

    1 mark

Answer: (i) RR, RB, RG, GR, GB, GG, YR, YB, YG; (ii) 1/9; (iii)(a) ₹330; (iii)(b) ₹385

Where the marks are

  • (i) Lists all 9 outcomes correctly (1 mark)
  • (ii) P(Making Purple) = 1/9 (1 mark)
  • (iii)(a) Number of winners = 11 (½ mark)
  • (iii)(a) Number of losers = 88 (½ mark)
  • (iii)(a) Fund = 88×5 − 11×10 = ₹330 (1 mark)
  • (iii)(b) Winners = 11 (½ mark)
  • (iii)(b) Losers = 88 (½ mark)
  • (iii)(b) Fund = 88×5 − 11×5 = ₹385 (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 30/5/1 (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.