December 16, 2009

科技與人類Question12.5(1)

骰子A分別出現6的機率是2/6=1/3
  2的機率是4/6=2/3

骰子B分別出現5的機率是3/6=1/2
  1的機率是3/6=1/2

骰子C分別出現4的機率是4/6=2/3
  0的機率是2/6=1/3

骰子D分別出現3的機率是6/6=1


骰子(A,B)
(6,5)
(6,1)     A>B: (6,5) (6,1) (2,1) -> 1/3*1/2+1/3*1/2+2/3*1/2=4/6=2/3
(2,5)     A<B: (2,5) -> 2/3*1/2=1/3
(2,1)

骰子(A,C)
(6,4)
(6,0)     A>C: (6,4) (6,0) (2,0)-> 1/3*2/3+1/3*1/3+2/3*1/3=5/9
(2,4)     A<C: (2,4)  -> 2/3*2/3=4/9
(2,0)

骰子(A,D)
(6,3) A>D: (6,3) -> 1/3*1=1/3
(2,3)     A<D: (2,3) -> 2/3*1=2/3

骰子(B,C)
(5,4)
(5,0)     B>C: (5,4) (5,0) (1,0) -> 1/2*2/3+1/2*1/3+1/2*1/3=2/3
(1,4)     B<C: (1,4) -> 1/2*2/3=1/3
(1,0)

骰子(B,D)
(5,3)     B>D: (5,3) -> 1/2*1=1/2 
(1,3)     B<D: (1,3) -> 1/2*1=1/2

骰子(C,D)
(4,3)     C>D: (4,3) -> 2/3*1=2/3
(0,3)     C<D: (0,3) -> 1/3*1=1/3


結論:
拿骰子A贏的機率是  2/3*5/9*1/3=7/9
   骰子B贏的機率是  1/3*2/3*1/2=2/3
   骰子C贏的機率是  4/9*1/3*2/3=8/81
   骰子D贏的機率是  2/3*1/2*1/3=1/9


  

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