lect7 - INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR...

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INDEPENDENCE OF TWO EVENTS N Outline INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR INDEPENDENT EVENTS INDEPENDENCE FOR THREE EVENTS INDEPENDENCE OF SEVERAL EVENTS 1 / 11 Xinghua Zheng Lect 7: Independence of Events
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INDEPENDENCE OF TWO EVENTS N INDEPENDENCE OF TWO EVENTS An event B is said to be independent of an event A (with P [ A ] > 0 and P [ A c ] > 0) if the occurrence or nonoccurence of A has no bearing on the chance for B to occur. Otherwise B is said to depend on A. More precisely, B is independent of A if P [ B | A ] = P [ B | A c ] . In general, what is the relation between P [ B ] , P [ B | A ] , and P [ B | A c ] ? P [ B ] = . If B is independent of A, then P [ B ] = = . 2 / 11 Xinghua Zheng Lect 7: Independence of Events
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INDEPENDENCE OF TWO EVENTS N EXAMPLE: TOSS TWO DICE B is independent of A P [ B | A ] = P [ B | A c ] P [ B ] = P [ B | A ] . Two fair dice are to be rolled. Let A be the event that their sum is 6: A = { ( 1 , 5 ) , ( 2 , 4 ) , ( 3 , 3 ) , ( 4 , 2 ) , ( 5 , 1 ) } B be the event that the first die is a 4. Is B independent of A? P [ B | A ] = ; P [ B ] = . As above, but change A to the event that the sum is 7. A = { ( 1 , 6 ) , ( 2 , 5 ) , ( 3 , 4 ) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) } Is B independent of A ? P [ B | A ] = ; P [ B ] = 3 / 11 Xinghua Zheng Lect 7: Independence of Events
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INDEPENDENCE OF TWO EVENTS N MULTIPLICATION RULE Suppose B is independent of A . What is
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This note was uploaded on 11/27/2011 for the course ISOM 3540 taught by Professor Zheu during the Spring '11 term at HKUST.

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lect7 - INDEPENDENCE OF TWO EVENTS MULTIPLICATION RULE FOR...

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