Baye's Theorem

Baye’s Theorem:

Let A₁, A₂, A₃, ...... A_n be n mutually exclusive events in a sample space S. Let E be any event in S overlapping each of these events A_i(i = 1, 2, 3, ...... n).

Event E is partitioned into n mutually exclusive events namely

A₁ ∩ E, A₂ ∩ E, A₃ ∩ E ....... A_{n ∩} E

⇒ E = (A₁ ∩ E) ∪ (A₂ ∩ E) ∪ (A₃ ∩ E) ....... ∪ (A_n ∩ E)