LrTrChVIIISIIISmplSpcsEvnts - Dr. Raja Latif. Math 131...

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Unformatted text preview: Dr. Raja Latif. Math 131 (043) Sec8.3 Pg:1 8 . 3 : Sample Spaces and Events EXPERIMENT An experiment is an activity with observable results. SAMPLE POINT : an outcome of an experiment. SAMPLE SPACE : the set consisting of all possible sample points of an experiment. EVENT : a subset of a sample space of an experiment. UNION OF TWO EVENTS The union of the two events E and F is the event E  F . 1 Dr. Raja Latif. Math 131 (043) Sec8.3 Pg:2 E  F  s  S : s  E or s  F . INTERSECTION OF TWO EVENTS The inter sec tion of the two events E and F is the event E  F . E  F  s  S : s  E & s  F . COMPLEMENT OF AN EVENT The complement of an event E is the event E c . E c   s  S : s  E   S  E . MUTUALLY EXCLUSIVE EVENTS E and F are mutually exclusive if E  F   . DeMORGAN’S LAWS:  E  F  c  E c  F c 2 Dr. Raja Latif. Math 131 (043) Sec8.3 Pg:3  E  F  c  E c  F c . (True for any number of events) In Exercise 1  6, let S   a , b , c , d , e , f  be a sample space of an experiment and let E   a , b  , F   a , d , f  , and G   b , c , e  be events of this experiment. 1.Find the events E  F and E  F . E  F   a , b , d , f  ; E  F   a  . 2.Find the events F  G and F  G . F  G   a , b , c , d , e , f  ; F  G   3.Find the events F c and F  G c . 3 Dr. Raja Latif. Math 131 (043) Sec8.3 Pg:4 F c   b , c , e  ; E  G c   a , b    a , d , f    a  4.Find the events E c and F c  G . E c   c , d , e , f  ; F c  G   b , c , e    b , c , e    b , c , e  . 5.Are the events E and F mutually exclusive? Since E  F   a  is not a null set, we conclude that E and F are not mutually exclusive. 6.Are the events E  F and E  F c mutually exclusive? E  F   a , b , d , f  and E  F c   a , b    b , c , e    b  ....
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