Ex1soln - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 1306 INTRODUCTORY STATISTICS (Sem 1 2008/ 2009) EXAMPLE CLASS 1 ANSWERS 1. a) PERMUTATIONS: Order is important. abc acb bac bca cab cba abd adb bad bda dab dba acd adc cad cda dac dca bcd bdc cbd cdb dbc dcb RULE: )! ( ! ) , ( r n n r n P = There are 24 1 2 3 4 ! 4 )! 3 4 ( ! 4 ) 3 , 4 ( = = = = x x x P ways
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b) COMBINATIONS: If we are NOT concerned with the order then: RULE: ! ) , ( ! )! ( ! ) , ( r r n P r r n n r n C = = Here, there are only () 4 1 2 3 1 2 3 4 )! 3 4 ( ! 3 ! 4 ) 3 , 4 ( 4 3 = = = = x x x x x C The committees are: a b c, a b d, a c d, b c d
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2. There are 8! = 40,320 ways of arranging 8 different books on a shelf. )! ( ! r n n P n r = therefore ! 8 ! 0 ! 8 8 8 = = P 3. There are 10 x 9 x 8 x 7 = 5,040 ways of ranking teams 1 st , 2 nd , 3 rd and 4 th . 7 8 9 10 ! 6 ! 10 10 4 x x x P = = 4. () 1365 1 2 3 4 12 13 14 15 )! 11 ( ! 4 ! 15 15 4 = = = x x x x x x committees. 5. 298 . 0 1292 385 ! 5 ! 15 ! 20 ! 2 ! 9 ! 11 ! 3 ! 6 ! 9 ) 5 , 20 ( ) 2 , 11 ( ) 3 , 9 ( ) ( = = = = x C xC C E P
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6. Draw a Venn diagram for each of the following: a) B B B c = B B complement b) A B A B “A OR B” U= “ Union c) B C “B AND C” B C = “ Intersection d) A C = A C ) ( C A De Morgan’s Law
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) Mutually exclusive events or DISJOINT e ( empty set ) A B is a subset of B robability of an event occurring A B= f) A B BBBBBBBB B A A NOTE: P
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Ex1soln - THE UNIVERSITY OF HONG KONG DEPARTMENT OF...

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