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"Eight Ball" is a game played… (Class 10 Maths 2023, Q38)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2023: question 38

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, 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

"Eight Ball" is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15.

[Photograph of pool balls lined up on a pool table with a cue stick.]

The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random.

Based on the above information, answer the following questions:

  1. (i)

    What is the probability that the drawn ball bears number 8?

    1 mark
  2. (ii)

    What is the probability that the drawn ball bears an even number?

    2 marks

  3. OR

    (ii)

    What is the probability that the drawn ball bears a number, which is a multiple of 3?

    2 marks
  4. (iii)

    What is the probability that the drawn ball is a solid coloured and bears an even number?

    1 mark

Figure in the paper: Photograph of pool balls lined up on a green pool table, with a cue stick at the left and a large ball in the foreground; the balls are numbered and show solid and striped designs. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

The cue ball is not in the bowl, so the total number of outcomes is 15.

Hint 2

List the numbers from 1 to 15 that satisfy each condition and count them.

Hint 3

Solid balls are numbered only 1 to 8, so look for even numbers within that range.

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) Total outcomes = 15 balls, and only one ball bears number 8.

    P(number 8) .

    1 mark

  2. (ii) The even numbers from 1 to 15 are 2, 4, 6, 8, 10, 12, 14, so there are 7 favourable outcomes.

    ½ mark

  3. (ii) P(even number) .

    1½ marks

  4. (ii) OR: The multiples of 3 from 1 to 15 are 3, 6, 9, 12, 15, so there are 5 favourable outcomes.

    ½ mark

  5. (ii) OR: P(multiple of 3) .

    1½ marks

  6. (iii) The solid coloured balls are numbered 1 to 8. Of these, the even-numbered ones are 2, 4, 6, 8, so there are 4 favourable outcomes.

    P(solid and even) .

    1 mark

Answer: (i) 1/15; (ii) 7/15 OR 1/3; (iii) 4/15

Where the marks are

  • P(number 8) (1 mark)
  • Lists the 7 even-numbered balls (½ mark)
  • P(even) (1½ marks)
  • OR part: lists the multiples of 3: 3, 6, 9, 12, 15 (½ mark)
  • OR part: P(multiple of 3) (1½ marks)
  • P(solid and even) (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 30/6/1 (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.