Probability 2

Event An event is any collection of outcomes of an experiment. Formally, any subset of the sample space is an event. Any event which consists of a single outcome in the sample space is called an elementary or simple event. Events which consist of more than one outcome are called compound events. It is represented by A,B,C …etc Set theory is used to represent relationships among events. In general, if A and B are two events in the sample space S, then (A union B) = 'either A or B occurs or both occur' (A intersection B) = 'both A and B occur' (A is a subset of B) = 'if A occurs, so does B' A' or = 'event A does not occur' (the empty set) = an impossible event S (the sample space) = an event that is certain to occur Example Experiment: rolling a dice once - Sample space S = {1,2,3,4,5,6} Events A = 'score < 4' = {1,2,3} B = 'score is even' = {2,4,6} C = 'score is 7' = = 'the score is < 4 or even or both' = {1,2,3,4,6} = 'the score is < 4 and even' = {2} A' or = 'event A does not occur' = {4,5,6}   Mutually Exclusive Events Two events are mutually exclusive (or disjoint) if it is impossible for them to occur together. And their intersection doesnot exit Formally, two events A and B are mutually exclusive if and only if If two events are mutually exclusive, they cannot be independent and vice versa. Examples Experiment: Rolling a die once Sample space S = {1,2,3,4,5,6} Events A = 'observe an odd number' = {1,3,5} B = 'observe an even number' = {2,4,6} = the empty set, so A and B are mutually exclusive.   Not Mutually Exclusive Events Two events are Not mutually exclusive (or joint) if it is possible for them to occur together and their intersection esit   Examples Experiment: Rolling a die once Sample space S = {1,2,3,4,5,6} Events A = 'observe an odd number' = {1,3,5} B = 'observe an number less than 5' = {1,2,3,4} {1,3} = so A and B are Not  mutually exclusive.