MathsCBSE Class 12 · Board exam 2025, set 65/7/1 · 2 marks · Very short answer

CBSE Class 12 Mathematics 2025: question 25(b)

Set in the CBSE Class 12 board exam of 2025, paper 65/7/1, section B, question 25(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(b) · 2 marks · Very short answerCompetency-basedProbability

In a village of 8000 people, 3000 go out of the village to work and 4000 are women. It is noted that 30% of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village ?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 65/7/1.

Hints

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

Hint 1

'Either … or' points to $P (A \cup B)$ .

Hint 2

The women who work outside are counted in both groups. Find how many there are using the 30% figure.

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.

Let A be the event that the person is a woman and B the event that the person works outside the village. The number of women working outside is $30%$ of $4000 = 1200$ . So $P (A) = \frac{4000}{8000} = \frac{1}{2}$ , $P (B) = \frac{3000}{8000} = \frac{3}{8}$ and $P (A \cap B) = \frac{1200}{8000} = \frac{3}{20}$ .
1½ marks
$P (A \cup B) = P (A) + P (B) - P (A \cap B) = \frac{1}{2} + \frac{3}{8} - \frac{3}{20} = \frac{20 + 15 - 6}{40} = \frac{29}{40}$
½ mark

Answer: $\frac{29}{40}$

Where the marks are

Finds $P (A) = \frac{1}{2}$ , $P (B) = \frac{3}{8}$ , $P (A \cap B) = \frac{3}{20}$ (1½ marks)
Uses the addition rule to get $\frac{29}{40}$ (½ 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 65/7/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 25(b)

Hints

Step-by-step solution

Revise the chapter

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