MathsCBSE Class 12 · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2026-27: question 17

From the official CBSE sample question paper for 2026-27, section A, question 17, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q17 · 1 mark · MCQProbability

A die is thrown twice. What is the probability that at least one number is 4, given the sum of the numbers appearing is a multiple of 5?

(A) $\frac{3}{5}$
(B) $\frac{4}{5}$
(C) $\frac{3}{7}$
(D) $\frac{4}{7}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

List all pairs whose sum is 5 or 10.

Hint 2

Count how many of these pairs contain a 4.

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 'sum is a multiple of 5'. Then $A = {(1, 4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)}$ , which has 7 outcomes.
Let $B$ be 'at least one 4'. Then $A \cap B = {(1, 4), (4, 1), (4, 6), (6, 4)}$ , which has 4 outcomes. So $P (B ∣ A) = \frac{4}{7}$ .
1 mark

Answer: 4/7, option (D)

Where the marks are

Lists the outcomes and computes the conditional probability (1 mark)

Revise the chapter

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

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 2026-27: every question, by section.

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CBSE Class 12 Mathematics sample paper 2026-27: question 17

Hints

Step-by-step solution

Revise the chapter

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