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Case Study – 1 Family… (Class 10 Maths Basic 2024, Q36)

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MathsCBSE Class 10 · Basic · Board exam 2024, set 430/5/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2024: question 36

Set in the CBSE Class 10 board exam of 2024, paper 430/5/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedProbability

Case Study – 1

Family structure : In a recent survey of this year, 51% of the families in the United States of America had no children, 20% had one child, 19% had two children, 7% had three children and 3% had four or more children. A family is selected at random.

(The page shows four illustrations of families with different numbers of children.)

Based on the above information, answer the following questions :

  1. (i)

    Find the probability that the selected family has two or three children.

    1 mark
  2. (ii)

    Find the probability that the selected family has more than one child.

    1 mark
  3. (iii)

    (a) Find the probability that the selected family has less than three children.

    2 marks

  4. OR

    (iii)

    (b) Find the probability that the selected family has more than two children.

    2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/5/1.

Hints

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

Hint 1

Treat the percentages as the number of favourable families out of 100.

Hint 2

List exactly which child-counts are included in each event, e.g. 'more than one' means 2, 3, 4 or more.

Hint 3

Add the matching percentages and divide by 100, then simplify.

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) Families with two or three children make up . So P(2 or 3 children)

    ½ mark

  2. (i)

    ½ mark

  3. (ii) More than one child means 2, 3, or 4 or more children. So P

    ½ mark

  4. (ii)

    ½ mark

  5. (iii)(a) Less than three children means 0, 1 or 2 children. So P

    1½ marks

  6. (iii)(a)

    ½ mark

  7. (iii)(b) More than two children means 3, or 4 or more children. So P

    1½ marks

  8. (iii)(b)

    ½ mark

Answer: (i) 13/50; (ii) 29/100; (iii)(a) 9/10; (iii)(b) 1/10

Where the marks are

  • (i) Adds 19% and 7% as favourable cases (½ mark)
  • (i) Gets 13/50 (½ mark)
  • (ii) Adds 19 + 7 + 3 (½ mark)
  • (ii) Gets 29/100 (½ mark)
  • (iii)(a) Adds 51 + 20 + 19 out of 100 (1½ marks)
  • (iii)(a) Gets 9/10 (½ mark)
  • (iii)(b) Adds 7 + 3 out of 100 (1½ marks)
  • (iii)(b) Gets 1/10 (½ 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 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.