HW25Answers(9.1) - Math331 Spring 2008 Instructor David...

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Math331, Spring 2008 Instructor: David Anderson Section 9.1 Homework Answers Homework: pgs. 383 - 384, #’s 1, 3, 5. 1. Let the number of hearts, diamonds, clubs, and spades be denoted by H , D , C , and S . We simply need to count the number of ways we can choose h hearts, d diamonds, c clubs, and s spades when h,d,c,s satisfy h + d + c + s = 13, and divide by the total number of 13 card combinations which is ( 52 13 ) . Simply by using the counting principle we get P { H = h,D = d,C = c,S = s } = braceleftBigg ( 13 h )( 13 d )( 13 c )( 13 s ) ( 52 13 ) if h + d + c + s = 13 0 otherwise . 3. We have p X,Y ( x,y ) = 1 162 2 summationdisplay z =1 xyz = 1 162 3 xy = 1 54 xy for x = 4 , 5 , y = 1 , 2 , 3 . p Y,Z ( y,z ) = 1 162 5 summationdisplay x =4 xyz = 1 162 9 yz = 1 18 yz, for y = 1 , 2 , 3 , z = 1 , 2 . p X,Z ( x,z ) = 1 162 3 summationdisplay y =1 xyz = 1 162 6 xz = 1 27 xz, for x = 4 , 5 , z = 1 , 2 . Using p Y,Z calculated above: E [ Y Z ] = 3 summationdisplay
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