Theorem 4.2. Bayes' Theorem. If E1, E2, E2 ..., E, are mutually disjoint events with •.. P (E:) # 0, (i = 1, 2, ..., n), then for any arbitrary event A which is a subset of ü E; such i = 1 that P (A)...

Prove the theorem

Extracted text: Theorem 4.2. Bayes' Theorem. If E1, E2, E2 ..., E, are mutually disjoint events with •.. P (E:) # 0, (i = 1, 2, ..., n), then for any arbitrary event A which is a subset of ü E; such i = 1 that P (A) > 0, we have P (Ε) P ( ΙΕ) P (E; I A) = P (E;) P (A | E;) Р (A) ;i = 1, 2, ..., n ..r Σ Ρ(Ε) P (AΑΙ Ε) i = 1 11