01:960:285 Lecture Notes - Lecture 11: Conditional Probability, Mutual Exclusivity, Joint Probability Distribution

• School: Rutgers University
• Department: Statistics and Biostatistic
• Course: 01:960:285
• Professor: Shyam Moondra

Document Summary

Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0. If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring. Only valid when the events are mutually exclusive. Given: p(a) = 0. 20, p(b) = 0. 70, a and b are disjoint. marginal is another word for totals -- it"s called marginal because they appear in the margins. The values in red are given in the problem. The rest of the values are obtained by addition and subtraction. In events which aren"t mutually exclusive, there is some overlap. When p(a) and p(b) are added, the probability of the intersection (and) is added twice. To compensate for that double addition, the intersection needs to be subtracted.