MathsCBSE Class 12 · Board exam 2025, set 65/1/1 · 3 marks · Short answer

CBSE Class 12 Mathematics 2025: question 30(b)

Set in the CBSE Class 12 board exam of 2025, paper 65/1/1, section C, question 30(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q30(b) · 3 marks · Short answerCompetency-basedProbability

For the vacancy advertised in the newspaper, 3000 candidates submitted their applications. From the data it was revealed that two third of the total applicants were females and other were males. The selection for the job was done through a written test. The performance of the applicants indicates that the probability of a male getting a distinction in written test is 0.4 and that a female getting a distinction is 0.35. Find the probability that the candidate chosen at random will have a distinction in the written test.

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

Hints

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

Hint 1

Split the applicants into males and females and write the probability of each group.

Hint 2

Use the theorem of total probability: $P (A) = \sum P (E_{i}) P (A ∣ E_{i})$ .

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.

Define the events. $E_{1}$ : the applicant is male. $E_{2}$ : the applicant is female. $A$ : the chosen candidate gets a distinction in the written test.
½ mark
$P (E_{1}) = \frac{1}{3}$ , $P (E_{2}) = \frac{2}{3}$ , $P (A ∣ E_{1}) = 0.4$ , $P (A ∣ E_{2}) = 0.35$ .
1 mark
By the theorem of total probability: $P (A) = P (E_{1}) P (A ∣ E_{1}) + P (E_{2}) P (A ∣ E_{2}) = \frac{1}{3} \times 0.4 + \frac{2}{3} \times 0.35$ .
1 mark
$P (A) = \frac{0.4 + 0.7}{3} = \frac{1.1}{3} = \frac{11}{30}$ .
½ mark

Answer: $P (distinction) = \frac{11}{30}$

Where the marks are

Defines the events $E_{1}$ , $E_{2}$ and $A$ (½ mark)
Writes the correct probabilities $\frac{1}{3}, \frac{2}{3}, 0.4, 0.35$ (1 mark)
Applies the total probability theorem (1 mark)
Gets $\frac{11}{30}$ (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 65/1/1: every question, by section.

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CBSE Class 12 Mathematics 2025: question 30(b)

Hints

Step-by-step solution

Revise the chapter

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