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

Q1. [1] § 14.2 Summary
Directions: A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. 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.
  1. A Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
  2. B Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of 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 30/6/1 Q20
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Model Answer

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

E₁ (less than 3) = {1, 2}, E₂ (greater than 3) = {4, 5, 6}. These are not complementary as they don't cover all outcomes (3 is excluded). Reason (R) is correct: P(E) + P(Ē) = 1.

Explanation

Complementary events must together cover the entire sample space with no outcome left out. Here, outcome {3} belongs to neither E₁ nor E₂, so their union ≠ sample space, making A false. The Reason is a standard, correct definition from the textbook (Summary point 6), so R is true.

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