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Mathematics — Standard (041) — CBSE Class 10 board question

Q1. [1] § 14.2 Summary
Assertion (A): The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event $E$, if $P(E) = 1$, then $E$ is called a sure event. Select the correct answer from the codes (A), (B), (C) and (D) given below.
  1. A Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  2. B Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  3. C Assertion (A) is true, but Reason (R) is false.
  4. D Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2025 30/1/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer

(D) Assertion (A) is false, but Reason (R) is true.

The Assertion is false because selecting any number from 1 to 20 is a sure event with P(E) = 1, not selecting a specific number (which would be 1/20). The Reason is true: P(E) = 1 implies a sure event.

Explanation

The Assertion is ambiguous but as stated — "probability of selecting a number at random from 1 to 20 is 1" — it appears to claim a specific selection has probability 1, which is false (it would be 1/20). However, if interpreted as selecting any number from the set, it is actually a sure event (P = 1). CBSE typically treats the Assertion here as false (implying a specific number), making option (D) correct. The Reason is directly from the textbook and is true. Focus on the distinction: sure event → P = 1; specific number → P = 1/20.

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Previous-year CBSE Grade 10 board exam questions, organised by subject and chapter, each with a model answer — free to read and print.