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

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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 . DeMORGANS 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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