Module 5: Total Probability Thrm & Bayes Thrm

Question 1

What is the total probability Thrm?

Answer 1

Let A_1,…,A_n be disjoint events that form a partition of the sample space and assume that P(A_i) > 0 for all i = 1, … , n. Then, for any event B, we have that:

P(B) = SUM(P(A_i ∩ B)) = SUM(P(A_i)*P(B|A_i))

Question 2

what is bayes thrm?

Answer 2

Let A_1, …, A_n be disjoint events that form a partition of the sample space, and assume that P(A_i) > 0 for all i. Then, for any event B such that P(B )> 0, we have

P(A_i|B) = P(A_i)P(B|A_i)/P(B)
= P(A_i)P(B|A_i)/SUM(P(A_i)P(B|A_i))