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Case Study 2: A group of… (Class 10 Maths 2026, Q37)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2026: question 37

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, 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 group of friends wanted to play cards with two identical packs together. While shuffling the cards, three cards are dropped. Rest of the cards are shuffled and one card is drawn at random. Assuming that the dropped cards were a queen of hearts, a ten of spades and an ace of clubs, answer the following questions :

  1. (i)

    Find the probability that the drawn card is a face card.

    1 mark
  2. (ii)

    Find the probability that the drawn card is either a king or a queen.

    1 mark
  3. (iii)(a)

    Do you think that the probability of getting a queen was higher if none of the cards were dropped? Justify your answer.

    2 marks

  4. OR

    (iii)(b)

    Find the probability that the drawn card is a jack. Compare it with the probability when none of the cards were dropped. In which case is the probability of getting a jack higher?

    2 marks

Figure in the paper: Photograph of a wooden box with two compartments, each containing a pack of playing cards. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

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

Hint 1

Two packs have 104 cards. How many remain after 3 are dropped?

Hint 2

Count the face cards, kings, queens and jacks in two packs, then remove any that were among the dropped cards (only a queen was a face card).

Hint 3

To compare two fractions, cross-multiply, or compare denominators when the numerators are equal.

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. Total cards in two packs . After 3 cards are dropped, cards left .

  2. (i) Face cards in two packs . One queen (of hearts) was dropped, so face cards left .

    1 mark

  3. (ii) Kings left and queens left , so favourable cards .

    1 mark

  4. (iii)(a) Yes, the probability was higher if no cards were dropped.

    ½ mark

  5. (iii)(a) With no cards dropped: .

    ½ mark

  6. (iii)(a) With cards dropped (7 queens left): .

    ½ mark

  7. (iii)(a) Compare by cross-multiplying: and .

    Since , . So getting a queen was more likely when no cards were dropped.

    ½ mark

  8. (iii)(b) No jack was dropped, so 8 jacks remain among 101 cards: .

    ½ mark

  9. (iii)(b) With no cards dropped: .

    ½ mark

  10. (iii)(b) The numerators are equal and , so .

    The probability of a jack is higher when the 3 cards were dropped.

    1 mark

Answer: (i) 23/101; (ii) 15/101; (iii)(a) Yes, 8/104 > 7/101; (iii)(b) 8/101, which is higher than 8/104 (higher when cards were dropped)

Where the marks are

  • (i) (1 mark)
  • (ii) (1 mark)
  • (iii)(a) Says yes (½ mark)
  • (iii)(a) Finds (½ mark)
  • (iii)(a) Finds (½ mark)
  • (iii)(a) Correct comparison with justification (½ mark)
  • (iii)(b) Finds (½ mark)
  • (iii)(b) Finds (½ mark)
  • (iii)(b) Compares and concludes higher when cards dropped (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 paper2026 board paper, set 30/3/1 (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.