In an experiment of throwing a die, Assertion (A): Event E_1: getting a number less than 3 and Event E_2: getting a number greater than 3 are complementary events. Reason (R): If two events E and F are complementary events, then P(E) + P(F) = 1. (A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2025: question 20

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedProbability

In an experiment of throwing a die,

Assertion (A): Event $E_{1}$ : getting a number less than 3 and Event $E_{2}$ : getting a number greater than 3 are complementary events.

Reason (R): If two events E and F are complementary events, then $P (E) + P (F) = 1$ .

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

List outcomes in each event.

Hint 2

Does every outcome belong to exactly one of them?

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.

$E_{1} = {1, 2}$ , $E_{2} = {4, 5, 6}$ ; outcome 3 is in neither, and $P (E_{1}) + P (E_{2}) = \frac{2}{6} + \frac{3}{6} = \frac{5}{6} \neq = 1$ . So A is false.
½ mark
For complementary events $P (E) + P (\overset{ˉ}{E}) = 1$ , so R is true. Option (D).
½ mark

Answer: Option (D)

Where the marks are

Shows E₁, E₂ not complementary (½ mark)
States R true (½ mark)

Revise the chapter

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

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 30/6/1 (Standard): 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.

CBSE Class 10 Mathematics Standard 2025: question 20

Hints

Step-by-step solution

Revise the chapter

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