MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Standard 2025: question 37

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, 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

Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose.

Answer the following questions if Rahul draws a card today :

(i)
What is the probability that Rahul draws a card with an even number ?
1 mark
(ii)
What is the probability that Rahul draws a card with an odd number less than 30 ?
1 mark
(iii)(a)
What is the probability that Rahul draws a card with a prime number between 50 and 74 ?
2 marks
OR
(iii)(b)
What is the probability that Rahul draws a card with an even number divisible by 5 ?
2 marks

Figure in the paper: A photograph of a hand drawing a folded paper card from a glass jar filled with small coloured folded cards (pink, yellow, blue). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

First count how many cards there are from 10 to 74, including both ends.

Hint 2

Count each required set carefully. The even numbers start at 10 and end at 74; the odd numbers below 30 start at 11.

Hint 3

An even number divisible by 5 is a multiple of 10. For the primes, test each odd number from 51 to 73.

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.

(i) Total number of cards $= 74 - 10 + 1 = 65$
½ mark
(i) The even numbers are $10, 12, \dots, 74$ , giving $\frac{74 - 10}{2} + 1 = 33$ cards.
$P (even) = \frac{33}{65}$
½ mark
(ii) The odd numbers less than 30 are $11, 13, \dots, 29$ , giving 10 cards.
$P = \frac{10}{65} = \frac{2}{13}$
1 mark
(iii)(a) The primes between 50 and 74 are $53, 59, 61, 67, 71, 73$ , so there are 6 favourable outcomes.
1 mark
(iii)(a) $P (prime between 50 and 74) = \frac{6}{65}$
1 mark
(iii)(b) The even numbers divisible by 5 are the multiples of 10: $10, 20, 30, 40, 50, 60, 70$ . There are 7 favourable outcomes.
1 mark
(iii)(b) $P (even and divisible by 5) = \frac{7}{65}$
1 mark

Answer: (i) 33/65; (ii) 2/13; (iii)(a) 6/65, (iii)(b) 7/65

Where the marks are

(i) Total outcomes = 65 (½ mark)
(i) $P (even) = \frac{33}{65}$ (½ mark)
(ii) $P = \frac{10}{65} = \frac{2}{13}$ (1 mark)
(iii)(a) Lists the 6 primes 53, 59, 61, 67, 71, 73 (1 mark)
(iii)(a) $P = \frac{6}{65}$ (1 mark)
(iii)(b) Lists the 7 multiples of 10 (1 mark)
(iii)(b) $P = \frac{7}{65}$ (1 mark)

Revise the chapter

Chapter: Probability (notes, formulas, where marks are lost and every past question)
Topic: Probability: Basic Terms and Classical Definition

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/2/1 (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.

CBSE Class 10 Mathematics Standard 2025: question 37

Hints

Step-by-step solution

Revise the chapter

More questions from Probability