(Pascal, B. ; 16~166) (de Me're' C. ; 1607~168) 80
01 8 % 1 0 0 0 60 70 1 100 100 61 7 68 7 88 1 100 1... A B A;B 81
A n(a;b) 1111 A n(a) A A;B n(a;b) 61 B 11111 = 1 n(a) 88 SAB 0 A B A B P(B A) S A B n(a;b) P(B A)= 11111 n(a) n(a) n(a;b) P(A)= 11 P(A;B)= 11111 n(s) n(s) n(a;b) 11111 n(a;b) P(B A)= = n(s) 11111 11111 n(a) n(a) 111 n(s) P(A;B) = 11111 P(A) A B P(A;B) P(B A)= 11111 P(A) P(A)>0 1 AB P(A)= 1P(A;B)= 1 10 ;1 0; P(B A)= 11= 1 ;!; 1 7 AB P(A)= 1P(B)= 1 P(A;B)= 1P(A B) 10 8
01 K D 0 %D 9% D K D A B 0 9 P(A)= 1 = 1P(A;B)= 1 100 100 A B 9 1 P(A;B) 100 9 P(B A)= 1111 = 1 = 1 P(A) 0 1 9 1 0 0 %0 % % (spam mail) 9 % % 100 100 8
DVD DVD 10 00 0 00 10 0 0 0 800 1... 1 P(A;B) P(B A)= 11111 P(A) P(A) P(A;B)=P(A)P(B A) P(A;B) P(A B)= 11111 P(B) P(B) P(A;B)=P(B)P(A B) AB AB P(A;B)=P(A)P(B A) P(A)>0) P(A;B)=P(B)P(A B) P(B)>0) AB P(A)= 1P(B)= 1P(A B)= 1P(B A) 8
0 6 A B 6 P(A)= 1 = 1 10 P(B A)= 1 9 P(A;B)=P(A)P(B A)= 1_ 1= 1 9 1 1 10 8 8
0 1 1 1. 1. 1 86
A B 1 A B P(B A)=P(B AÇ )=P(B)= 1 A B P(B A)=P(B AÇ )=P(B)A B A B P(A;B)=P(A)P(B A)=P(A)P(B) P(A)>0 P(A;B)=P(A)P(B) P(A)>0 P(A;B)=P(A)P(B A) P(B)=P(B A) A B A B P(B A)= 1P(B AÇ )= 1 A B P(B A)+P(B AÇ )A B A B P(A;B)=P(A)P(B) P(A)>0P(B)>0 87
01 A B6 C A B B C A C A B P(A;B)=P(A)P(B) A B P(A;B)+P(A)P(B) A={}B={6}C={16} P(A)= 1P(B)= 1P(C)= 1 A;B={}B;C={6}A;C={} P(A;B)= 1P(B;C)= 1P(A;C)= 1 6 6 P(A;B)= 1+P(A)P(B)= 1 A B 6 P(B;C)= 1+P(B)P(C)= 1 B C 6 P(A;C)= 1=P(A)P(C) A C 1 1 10 10 A B1 C A B B C A C A B 0<P(A)<10<P(B)<1 A BÇ AÇ B AÇ BÇ AB AB 0<P(A)<10<P(B)<1 88
1 1. 1 1.. 1 1 1_ 1_ 1 _ 1 6 6 6 6 1 C 1 { } { } 1 1 1 6 6 6 1 C 1 C { } { } 1 1 6 6 1 6 89
A p n A r «C p r (1-p) n-r r=0, 1, yn 0 7 10 1 10 10 10 7 C { } { } 9 087 1 1 =10_ 11_ 11= 11 10 10 1000 100 10000 087 11 10000 80 % 0 % A 8 B 16 A B 90
171 1 ab a+bæ10aæ 01 1 16 1 6 19 10 01 10 1 1 01 ABC 10 0 70 80 9 10 0 0 91
171 1 1 1 7 01 01 ABC 0 A B C A B 0 0.06 0 9
17 1 A B A B B A B 01 10 6 01 A 101 A A A 111 a+b a b _10å 0 P 1 ABCD 0 1 D A C B A P A 9
(Monty Hall) 1 http://www.grand illusions.com/simulator/montysim.htm (keep) (change) 00 9
1 A B P(A;B) P(B A)= 1111 P(A)>0 P(A) S A n(a) A P(A)= 111 = 11111111111 n(s) S n A r n n r n 1 p p A n S A 0 P(A) 1 A=S P(S)=1 A=Δ P(A)=0 AB P(A'B)=P(A)+P(B)-P(A;B) AB P(A'B)=P(A)+P(B) AB P(A;B)=P(A)P(B A) P(A)>0 P(A;B)=P(B)P(A B) P(B)>0 A B P(B A)=P(B AÇ )=P(B) A B A B P(B A)+P(B AÇ ) A B A B P(A;B)=P(A)P(B) P(A)>0P(B)>0 A p n A r nc r p r (1-p) n-r (r=01yn) A A C P(A C )=1-P(A) P(A)P(B A) 9
1 1 1 1 8 1 1 1 1 1 A={1y7} 10 1 9 1 1 1 11 99 9 1 1 99 1 6 6 1 1 1 1 1 7 81 81 1 1 16 7 81 1 1 1 7 7 8 1 1 7 8 A B P(A)-P(B)= 1P(A)P(B)= 1 6 6 7 10 1 P(A'B) 1 1 1 6 1 1 6 6 8 A B P(A)= P(A;B C 1 )= 1 P(A'B) 1 1 1 1 1 7 7 8 1 1 1 1 1 1 1 11 1 96
9 1 1 1 1 606 607 608 1 1 1 a 6 6 6 1 9fi 609 1 1 1 6 1 a 17 10 17 1 1 1 16 6 1 1 18 19 1 AB AB 11 A 11 0 9 1 A 1 B A B 1 1 16 AB P(A)= 1 P(B)= 1P(A B)= 1P(AÇ BÇ ) 97
Engineering 18 Buffon 1707~1788 1 1 http://www.efg.com/lab 1 p (%) 10.000000 7. 10 8.876 9.76 10 6.116 0.88 10 660.16 0.097 10fi 667.10999 0.019 10fl 67.1866 0.100 10 6661.11 0.00 10 6669.116 0.001 98
99 % 1 99 % 1% 100 1 100 100 99 % 100 99 1 100 999900 99 % 999900 99 % 98 9901 999900 1% 9999 99+9999=10098 99 1% 0 01 % 1 1% 1001 98 9901 (0 0001 %) Real Life 99