Chapter 14 — Probability

Probability quantifies the chances of event occurrence 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.

Chapter 14 introduces the axiomatic approach to probability, defining events as subsets of a sample space and classifying them into simple, compound, impossible, and sure events. Key concepts include mutually exclusive events (where A ∩ B = φ), exhaustive events (where E₁ ∪ E₂ ∪ ... ∪ Eₙ = S), and complementary events. The chapter develops three fundamental axioms: P(E) ≥ 0 for any event, P(S) = 1, and P(E ∪ F) = P(E) + P(F) for mutually exclusive events. For equally likely outcomes, P(A) = n(A)/n(S). The addition rule P(A ∪ B) = P(A) + P(B) - P(A ∩ B) extends to three events, and the complement rule states P(A') = 1 - P(A).

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)