12/7/20151 Math b Conditional Probability, Independency, Bayes Theorem

Conditional Probability (Sec. 3.6) If A and B are any events in S and P(B) ≠ 0, then the conditional probability of A given B is P(A|B) 12/7/20152

Conditional probability If A and B are any events in S and P(B) ≠ 0, then the conditional probability of A given B is 12/7/20153

Probability of Intersection (Product Rule) Using the conditional probability we can find P(AB) as  P(AB) = P(A|B)P(B), if P(B) ≠ 0 or  P(AB) = P(B|A)P(A), if P(A) ≠ 0 12/7/20154

Independent Events If P(A|B) = P(A) or P(B|A) = P(B), then A and B are called INDEPENDENT events. And hence: Two events A and B are independent if and only if P(AB) = P(A) P(B) 12/7/20155

Rule of Total Probability If B 1, B 2, B 3, …, B n are mutually exclusive events of which one must occur, then 12/7/20156

Bayes’ Theorem (Sec. 3.7) 12/7/20157 B 1, B 2, B 3, …, B n are mutually exclusive events of which one must occur. A is a n event. Then for any r = 1, 2, …, n