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tutorial02 - ISMT 111 BUSINESS STATISTICS TUTORIAL 2...

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1 ISMT 111 B USINESS S TATISTICS T UTORIAL 2 created by Andrew Yam Terminology Experiment: obtaining one observation Sample Space ( S ): the set of all possible outcomes of an experiment Simple Event: an element of the sample space Event: a subset of the sample space General Properties of Probabilities If A is an event, then ( 29 1 0 A P . ( 29 1 = S P If the set of simple events E 1 , E 2 , . . ., E r represents the sample space S for an experiment, then ( 29 1 1 1 = = r i E P . If A occurs when one of a set of k simple events E 1 , E 2 , . . ., E k occurs, then ( 29 ( 29 ( 29 ( 29 k E P E P E P A P + + + = ... 2 1 . Event Composition and Event Relations Intersection of A and B , denoted by AB (also as B A ) is the event that both A and B occur. Union of A or B , denoted by B A is the event that A or B or both occur. Complement of A , denoted by A (also, c A or ' A ), consists of all the simple events in the sample space that are not in A . ( 29 ( 29 A P A P - = 1 Two events A & B are said to be disjoint (or mutually exclusive) if they cannot occur simultaneously, i.e. ( 29 0 = AB P . Additional Rule of Probability
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2 ( 29 ( 29 ( 29 ( 29 AB P B P A P B A P - + = If A & B are mutually exclusive, then ( 29 ( 29 ( 29 B P A P B A P + = . Conditional probability The conditional probability of B given that A has occurred is ( 29 ( 29 ( 29 A P AB P A B P = | , for ( 29 0 A P .
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