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A lot consists of 200… (Class 10 Maths Basic 2025, Q31)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 31

Set in the CBSE Class 10 board exam of 2025, paper 430/1/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerCompetency-basedProbability

A lot consists of 200 pens of which 180 are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of 100 pens containing 80 good pens is mixed with the previous lot of 200 pens. The shopkeeper now draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/1/1.

Hints

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

Hint 1

The customer refuses only a defective pen. How many defective pens are in the first lot?

Hint 2

After mixing, count the total pens and the good pens together.

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. Defective pens in the first lot . The customer will not buy a defective pen, so P(customer will not buy) .

    1 mark

  2. After mixing the two lots: total pens and good pens .

    1 mark

  3. P(customer will buy) .

    1 mark

Answer: 1/10; 13/15

Where the marks are

  • P(will not buy) (1 mark)
  • Total pens 300 and good pens 260 (1 mark)
  • P(will buy) (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 paper2025 board paper, set 430/1/1 (Basic): 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.