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Case Study -3 Excessive… (Class 12 Maths SQP 2025-26, Q38)

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MathsCBSE Class 12 · Sample paper, session 2025-26 · 4 marks · Case-based

CBSE Class 12 Mathematics sample paper 2025-26: question 38

From the official CBSE sample question paper for 2025-26, 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

Case Study -3

Excessive use of screens can result in vision problems, obesity, sleep disorders, anxiety, low retention problems and can impede social and emotional comprehension and expression. It is essential to be mindful of the amount of time we spend on screens and to reduce our screen-time by taking regular breaks, setting time limits, and engaging in non-screen-based activities.

In a class of students of the age group 14 to 17, the students were categorised into three groups according to a feedback form filled by them. The first group constituted of the students who spent more than 4 hours per day on the mobile screen or the gaming screens, while the second group spent 2 to 4 hours /day on the same activities. The third group spent less than 2 hours /day on the same. The first group with the high screen time is 60% of all the students, whereas the second group with moderate screen time is 30% and the third group with low screen time is only 10% of the total number of students. It was observed that 80% students of first group faced severe anxiety and low retention issues, with 70% of second group, and 30% of third group having the same symptoms.

  1. I

    What is the total percentage of students who suffer from anxiety and low retention issues in the class?

    2 marks
  2. II

    A student is selected at random, and he is found to suffer from anxiety and low retention issues. What is the probability that he/she spends screen time more than 4 hours per day?

    2 marks

Figure in the paper: Illustration of three children sitting on a sofa using mobile phones, with a television showing cartoon characters behind them. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

Name the three screen-time groups as events and write their probabilities along with the conditional probabilities of symptoms.

Hint 2

Part I needs the theorem of total probability.

Hint 3

Part II reverses the condition, so use Bayes' theorem with your answer from Part I as the denominator.

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. Define the events:

    • : the student spends more than 4 h/day on screens
    • : the student spends 2–4 h/day on screens
    • : the student spends less than 2 h/day on screens
    • : the student has anxiety and low retention issues

    Then , , .

    Also , , .

  2. I. By the theorem of total probability:
    .

    So .

    1 mark

  3. I (contd.) .

    Hence 72% of the students suffer from anxiety and low retention issues.

    1 mark

  4. II. By Bayes' theorem:

    1 mark

  5. II (contd.) .

    1 mark

Answer: I. 72%. II.

Where the marks are

  • Applies the total probability formula with the correct values (1 mark)
  • Obtains , i.e. 72% (1 mark)
  • Applies Bayes' theorem for (1 mark)
  • Gets (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26: 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.