A bag contains 6 red, 4 black and some white balls. (i) Find the number of white balls in the bag if the probability of drawing a white ball is 1/3. (ii) How many red balls should be removed from the bag for the probability of drawing a white ball to be 1/2?

MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 31

From the official CBSE sample question paper for 2023-24, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerProbability

A bag contains 6 red, 4 black and some white balls.

(i)
Find the number of white balls in the bag if the probability of drawing a white ball is $\frac{1}{3}$ .
1 mark
(ii)
How many red balls should be removed from the bag for the probability of drawing a white ball to be $\frac{1}{2}$ ?
2 marks

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Probability = favourable outcomes ÷ total outcomes. Write the total number of balls in terms of the unknown.

Hint 2

For (ii), the number of white balls stays at 5, but the total falls by the number of red balls removed.

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) Let the number of white balls be $x$ . Total balls $= 6 + 4 + x = 10 + x$ .
$P (white) = \frac{x}{10 + x} = \frac{1}{3} \Rightarrow 3 x = 10 + x \Rightarrow x = 5$
There are 5 white balls.
1 mark
(ii) Let $y$ red balls be removed. Total balls $= (6 - y) + 4 + 5 = 15 - y$ .
$P (white) = \frac{5}{15 - y} = \frac{1}{2}$
1 mark
$\Rightarrow 10 = 15 - y \Rightarrow y = 5$
So 5 red balls should be removed.
1 mark

Answer: (i) 5 white balls; (ii) 5 red balls should be removed

Where the marks are

(i) Forms $\frac{x}{10 + x} = \frac{1}{3}$ and gets $x = 5$ (1 mark)
(ii) Forms $\frac{5}{15 - y} = \frac{1}{2}$ (1 mark)
(ii) Solves to get $y = 5$ (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 paperSample paper 2023-24 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2023-24: question 31

Hints

Step-by-step solution

Revise the chapter

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