STATS 101B Lecture Notes - Lecture 4: Collectively Exhaustive Events, Venn Diagram
Document Summary
The addition rule tells us, for events a and b, how to compute. P(a or b) = p(a) + p(b) p(a and b) In words, we add the probability of a and the probability of. B, and then remove the probability of a and b so as to not double count. The addition rule can be visualized with the aid of a venn diagram: (we add the area of a and the area of b, and then we subtract. A b, so as to not double count it. ) If a and b are mutually exclusive, then p(a and b) = 0, and the addition rule simplifies: The total probability rule tells us how to divide up a probability p(a) using the joint probabilities p(a and b) and p(a and bc): p(a) = If we have a, and any collection of mutually exclusive and collectively exhaustive events b. , bk, then: + + p(a and bk).
