Chapter 14 — Probability

Chapter 14 of the Class 11 Maths NCERT textbook, "Probability", quantifies the chances of events through axiomatic rules: for any event E, 0 ≤ P(E) ≤ 1, with P(S) = 1 for the sample space and P(φ) = 0 for the impossible event.

• Events as subsets of a sample space — The chapter frames every event as a subset of the sample space and classifies events as simple, compound, impossible or sure, giving a set-theoretic language for describing what can happen in an experiment.
• The axiomatic foundation — Rather than relying only on counting, it builds probability from three axioms, defining relationships like mutually exclusive and exhaustive events so probability rests on a rigorous logical base.
• Rules for combining probabilities — From the axioms it derives working tools — the equally-likely ratio, the addition rule for unions, and the complement rule — that let you compute the probability of combined and opposite events.

1. 01An event is any subset of a sample space; simple events contain one sample point, compound events contain multiple sample points
2. 02Mutually exclusive events cannot occur together (A ∩ B = φ); exhaustive events cover the entire sample space when combined
3. 03The three axioms of probability: P(E) ≥ 0, P(S) = 1, and P(E ∪ F) = P(E) + P(F) for mutually exclusive events
4. 04For equally likely outcomes, probability of event A equals the ratio n(A)/n(S) of favorable to total outcomes
5. 05The union rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B); complement rule: P(A') = 1 - P(A)