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Probability

NCERT Class 11 Mathematics Chapter 14

Probability for Class 11 Maths and JEE: events and their types, the algebra of events and the axiomatic approach to probability, with solved examples.

2 topics Updated 8 Nov 2026

For: Class 11 and JEE

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 14 “Probability”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.3 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Events

    Sample space, types of events, A or B, not A, mutually exclusive and exhaustive events, with solved examples.

    NCERT Section 14.1 15 min read 6 solved examples 12 practice questions

  2. Axiomatic approach to probability

    The three axioms, equally likely outcomes, the addition theorem, P(not A), formulas and solved examples.

    NCERT Section 14.2 17 min read 7 solved examples 13 practice questions

Key formulas in this chapter

Events

  • not A = A′ = S − A
  • A or B = A ∪ B; A and B = A ∩ B
  • A but not B = A − B = A ∩ B′
  • neither A nor B = A′ ∩ B′ = (A ∪ B)′
  • mutually exclusive: A ∩ B = ϕ
  • exhaustive: E ∪ E ∪ … ∪ E = S

Axiomatic probability

  • P(E) ≥ 0, P(S) = 1
  • P(E ∪ F) = P(E) + P(F) if E ∩ F = ϕ
  • P(ϕ) = 0
  • equally likely: P(E) = n(E)/n(S)
  • P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
  • P(not A) = 1 − P(A)
  • P(A ∩ B′) = P(A) − P(A ∩ B)
  • P(A′ ∩ B′) = 1 − P(A ∪ B)

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