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

Q1. [1] § Chapter Opening and Epigraph § 14.2 Summary
Probability of happening of an event is denoted by p and probability of non-happening of the event is denoted by q. Relation between p and q is
  1. A p + q = 1
  2. B p = 1, q = 1
  3. C p = q - 1
  4. D p + q + 1 = 0
Previously asked in CBSE board exam
2023 30/1/1 Q16
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Model Answer

Option A: p + q = 1

Since p = P(E) and q = P(not E), and P(E) + P(not E) = 1, the relation between p and q is p + q = 1.

Source: Chapter 14, Section 14.2 (Summary, Point 6)

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Explanation

The textbook states: "For any event E, P(E) + P(Ē) = 1, where Ē stands for 'not E'." Here p = P(E) and q = P(Ē), so p + q = 1. This is the complementary events rule — the most fundamental relation in probability. Examiners expect you to directly identify option A without calculation.

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