A bag contains 30 balls out of which ‘m’ number of balls are blue in colour. (i) Find the probability that a ball drawn at random from the bag is not blue. (ii) If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be 5/4 times the probability of drawing a blue ball in the first case. Find the value of m.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 30

Set in the CBSE Class 10 board exam of 2026, paper 30/4/1, section C, question 30, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30 · 3 marks · Short answerProbability

A bag contains 30 balls out of which ‘m’ number of balls are blue in colour.

(i)
Find the probability that a ball drawn at random from the bag is not blue.
0 marks
(ii)
If 6 more blue balls are added in the bag, then the probability of drawing a blue ball will be $\frac{5}{4}$ times the probability of drawing a blue ball in the first case. Find the value of m.
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/4/1.

Hints

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

Hint 1

Probability = favourable outcomes ÷ total outcomes; adding balls changes both the blue count and the total.

Hint 2

Old P(blue) $= \frac{m}{30}$ , new P(blue) $= \frac{m + 6}{36}$ ; set the new one equal to $\frac{5}{4}$ of the old one.

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) Number of balls that are not blue $= 30 - m$ . P(not blue) $= \frac{30 - m}{30}$ (or $1 - \frac{m}{30}$ ).
1 mark
(ii) After adding 6 blue balls: total balls $= 36$ , blue balls $= m + 6$ . So P(blue) $= \frac{m + 6}{36}$ .
1 mark
Given: $\frac{m + 6}{36} = \frac{5}{4} \times \frac{m}{30} = \frac{m}{24}$ .
½ mark
$24 (m + 6) = 36 m \Rightarrow 24 m + 144 = 36 m \Rightarrow 12 m = 144 \Rightarrow m = 12$ .
½ mark

Answer: (i) $\frac{30 - m}{30}$ ; (ii) $m = 12$

Where the marks are

P(not blue) $= \frac{30 - m}{30}$ (1 mark)
New P(blue) $= \frac{m + 6}{36}$ (1 mark)
Forms equation $\frac{m + 6}{36} = \frac{5}{4} \times \frac{m}{30}$ (½ mark)
Solves to get $m = 12$ (½ mark)

Revise the chapter

Chapter: Probability (notes, formulas, where marks are lost and every past question)
Topic: Properties of Probability and Complementary Events

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 30/4/1 (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 2026: question 30

Hints

Step-by-step solution

Revise the chapter

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