# lect3 - SOME RULES OF PROBABILITY EXAMPLES THE BIRTHDAY...

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SOME RULES OF PROBABILITY EXAMPLES Outline SOME RULES OF PROBABILITY EXAMPLES THE BIRTHDAY PROBLEM GENERALIZATIONS OF BIRTHDAY PROBLEM 1 / 11 Xinghua Zheng Lect 3: Some Rules for Computing Probabilities

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SOME RULES OF PROBABILITY EXAMPLES GENERAL PROBABILITY MODELS A probability model has three components: 1. a sample space S, 2. a collection of events, and 3. a probability distribution P over the events. A probability distribution P satisﬁes the following axioms: 1. P is nonnegative: P [ E ] 0 for all events E ; 2. P is additive: if the events E 1 , E 2 , . . . are mutually exclusive , then P [ i E i ] = X i P [ E i ]; 3. P has total mass 1: P [ S ] = 1 . 2 / 11 Xinghua Zheng Lect 3: Some Rules for Computing Probabilities
SOME RULES OF PROBABILITY EXAMPLES EXAMPLE: DRAW TWO CARDS Two cards are drawn successively from a well shufﬂed deck of 52 cards. Find the probability that the second card is higher in rank than the ﬁrst card. 1. Let H = {2nd higher than 1st}; L = {2nd lower than 1st}; and Q = {2nd = 1st}. 3 / 11 Xinghua Zheng Lect 3: Some Rules for Computing Probabilities

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SOME RULES OF PROBABILITY EXAMPLES SOME SIMPLE RULES OF PROBABILITY The rule of differences : If A and B are events such that A B , then P ( B \ A ) = , because the events A and B \ A are , and their union is , so
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lect3 - SOME RULES OF PROBABILITY EXAMPLES THE BIRTHDAY...

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