MathsCBSE Class 12 · Sample paper, session 2025-26 · 3 marks · Short answer

CBSE Class 12 Mathematics sample paper 2025-26: question 31

From the official CBSE sample question paper for 2025-26, 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

Two students Mehul and Rashi are seeking admission in a college. The probability that Mehul is selected is 0.4 and the probability of selection of exactly one of the them is 0.5. Chances of selection of them is independent of each other. Find the chances of selection of Rashi. Also find the probability of selection of at least one of them.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

'Exactly one' means Mehul but not Rashi, or Rashi but not Mehul.

Hint 2

For independent events, $P (A \cap \overset{ˉ}{B}) = P (A) P (\overset{ˉ}{B})$ ; for 'at least one' use the complement.

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: Mehul is selected, B: Rashi is selected; A, B independent. $P (A) = 0.4$ , $P (B) = x$ . Exactly one selected: $P (A \cap \overset{ˉ}{B}) + P (\overset{ˉ}{A} \cap B) = 0.5$ .
1 mark
$P (A) P (\overset{ˉ}{B}) + P (\overset{ˉ}{A}) P (B) = 0.5 \Rightarrow 0.4 (1 - x) + 0.6 x = 0.5 \Rightarrow 0.2 x = 0.1 \Rightarrow x = 0.5$ . So $P (Rashi selected) = 0.5$ .
1 mark
$P (at least one) = 1 - P (\overset{ˉ}{A} \cap \overset{ˉ}{B}) = 1 - P (\overset{ˉ}{A}) P (\overset{ˉ}{B}) = 1 - 0.6 \times 0.5 = 0.7$ .
1 mark

Answer: Rashi: 0.5; at least one: 0.7

Where the marks are

Defines events and writes the 'exactly one' condition (1 mark)
Uses independence to get $P (B) = 0.5$ (1 mark)
Probability of at least one $= 0.7$ (1 mark)

Revise the chapter

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

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 2025-26: every question, by section.

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CBSE Class 12 Mathematics sample paper 2025-26: question 31

Hints

Step-by-step solution

Revise the chapter

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