# lect6 - THE MULTIPLICATION RULE BAYES RULE Outline THE...

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THE MULTIPLICATION RULE BAYES’ RULE Outline THE MULTIPLICATION RULE BAYES’ RULE 1 / 11 Xinghua Zheng Lect 6: Multiplication Rule; Bayes’ Rule

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THE MULTIPLICATION RULE BAYES’ RULE THE MULTIPLICATION RULE How can you ﬁnd the chance that two events A and B both occur simultaneously? P [ B | A ] = P [ A B ] P [ A ] P [ A B ] = × . The chance that three events A, B, and C occur simultaneously? P [ A B C ] = × = P [ A ] × P [ B | A ] × P [ C | A B ] A tree diagram for this formula: What is the generalization to n events? These formulas are known as the multiplication rule . 2 / 11 Xinghua Zheng Lect 6: Multiplication Rule; Bayes’ Rule
THE MULTIPLICATION RULE BAYES’ RULE ANOTHER QUESTION ABOUT BRIDGE An ordinary deck of 52 cards is randomly divided into 4 hands of 13 cards each. Find the chance that each hand has exactly 1 ace. Deﬁne events A 1 , A 2 , A 3 and A 4 as follows: A 1 = { the A is in any one of the hands } , A 2 = { the A & A are in different hands } , A 3 = { the A , A & A are in different hands } , A 4 = { all 4 aces are in different hands } . Think about dealing out the 4 aces into 52 slots, divided into 4 hands: , , , The A could go anywhere and is guaranteed to be in some hand. So P [ A 1 ] = : , , A , Given A 1 , the A could go into any of slots, of which put it in a different hand. So P [ A 2 | A 1 ] = : A , , A , Similarly, P [ A 3 | A 1 A 2 ] = , and P [ A 4 | A 1

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lect6 - THE MULTIPLICATION RULE BAYES RULE Outline THE...

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