申論題

5.

(1). Prove Bayes' Theorem:
The posterior probability P(Aᵢ|Bⱼ) of outcome Aᵢ occurring, given
information outcome Bⱼ occurs, is obtained as follows:
P(Aᵢ|Bⱼ) = , i = 1, 2,...
where P(Bⱼ|Aᵢ) is the conditional probability for the outcome Bⱼ occurring,
given outcome Aₖ (k = 1,2,...) occurs. (8%)