II 2 72

90 % 0 % 74

80 % 80 % 90 % 0 % 00 90 0 80 % 0 80 % 8 20 % 9020 % 8 268 ;2 6;=0307y 3 % (90) 72 8 (0) 2 8 74 26 75

0 02 2 5 25 A B AB AB pq A B p+q 2 5 5 2 np r =n(n-)y(n-r+) np r n! nc r = 2 = 22 r! r!(n-r)! 76

P(A) 00 500 H T (H) (T) (H) (T) 2 S S A A S S={23456} A A={246} S A 2 4 3 6 5 9 9 8 77

A B A B S AB A B A'B A B A;B S S A B A B A'B A;B AB A;B=Z A A A AÇ A;A C =Z AA C S A B S A AÇ A B A={246}B={35} A;B=Z AB A B B A 4 5 78

A3 B6 C AC A B S S={23456} A={35}C={6} A;C=Z A C A={35}B={36} A C ={246}B C ={245} A C ;B C ={24}+Z A B A B C AB BC CA A BC 0 0 6 A BC AB AC 79

n A r n n A r n 4 p p n n n 4 n r n A 420 300 2 203 3 203 3 30 39 5 9 20 29 30 39 40 49 50 59 60 26 3820 5874 6728 5585 373 25396 (http://kosis.kr) 253960003039 5874000 5874000 4 023 25396000 023 023 80

366279 2940 44726 34083 2853 57869 69350 355 8824 35077 2360 50808 2400 7457 380606 8499 265006 e- 20 (http://www.index.go.kr) P(A) P Probability AA P(A) 23456 6 (Laplace, P. S. ; 749~827) ;6!; S AP(A) S n(s) A n(a) n(a) P(A)= 25 n(s) A S A S={23456}A={35} n(a) A P(A)= 25=;6#;=;2!; n(s) 8

3 6 7 3 2 6 4 5 S 7 A S={()(2)(3)y(65)(66)} n(s)=6_6=36 A={(6)(25)(34)(43)(52)(6)} n(a)=6 n(a) P(A)= 23 =;3 6;=;6!; n(s) ;6!; 0 4 5 2 3 3 2 7 3 C =35 53 C =0 ;3!5);=;7@; 5 22 C _ C =5 ;3 5;=;7!; ;7@; ;7!; 6 ABCDEF ABC 82

na n n 5 5 2 0 3 2 n 2 nc 2 24 2 C 5 2 03 2 2 2 ; 0; 24 nc 2 =; 0; n(n-) 5 2 =3n 2 -n-6=0 (n-3)(n+2)=0 0 n 5 n=3 3 3 5 C 2 n 2 3 9000 4000 n AS Z,A,S 0 n(a) n(s) n(s) n(a) 0 24 0 P(A) n(s) S Z n(s) n(z) P(S)= 24 =P(Z)= 24 =0 n(s) n(s) 83

A 0 P(A) SP(S)= ZP(Z)=0 36 37 0 4 2 2 3 A B 2 C AB BC CA 2 2 6 AB P(A)=0 P(B)= 84

30 5 5 3 2 3 S AB AB n(a)n(b) n(a'b)=n(a)+n(b)-n(a;b) yy A B n(s) n(a'b) n(a) n(b) n(a;b) 24 = 244 + 244-24 n(s) n(s) n(s) n(s) P(A'B)=P(A)+P(B)-P(A;B) AB P(A;B)=0 P(A'B)=P(A)+P(B) 85

AB P(A'B)=P(A)+P(B)-P(A;B) AB P(A'B)=P(A)+P(B) A B A={35}B={235} A;B={35} A'B P(A'B)=P(A)+P(B)-P(A;B)=;6#;+;6#;-;6@;=;3@; ; 0; ;5@; ; 0; 5 4 2 2 2 AB AB 2 A2 B C 5 C P(A)= 25= 4 P(B)= 25= ªC 8 ªC 6 AB 5 4 P(A'B)=P(A)+P(B)= 4 + = 8 6 9 4 9 4 3 3 2 86

A P(A) A P(A C ) S A AÇ A A C P(A C )=;4#; P(A) P(A C )=;4#;=-;4!;=-P(A) S AA C A'A C =S AA C =P(S)=P(A'A C )=P(A)+P(A C ) P(A C )=-P(A) A A C P(A C )=-P(A) 2 3 3 3 P(A) P(A C ) A 3 C A C P(A C )= 2 =;2 0; C P(A)=-P(A C )=-;2 0;=;2!0(; ;2!0(; 87

5 ABCDE A B 0 0 7 8 2 2 6 2 2 3 5 2 5 3 6 4 5 2 4 3 6 88

. 2. AB A;B=Z AB 3. A A A A C 4. n A r n n r n 3 p pa n 5. A A 6. S n(s)a n(a) n(a)p(a)= 32 A n(s) 0 200 0 7 4992 200 2 0 8 2250 3 258 9 8922 4 05 0 472 6 5 5658 643 6 7895 2 0 0522 e- 200 (http://www.index.go.kr) 02 89

03 6 ABCDEF 3 C 04 05 3 2 2 06 3 3 2 4 07 00 5 08 '2 90

(birthday problem) 2 365 ;36!5; 365 23 50 %57 99 % 23 2A A A A C 23 365 23 365 23 23 P P P(A C )= 24 0493 P(A)0507 365 23 20507 n 2 P n P n P n =- 2 (2 n 365) 365 n np n P«0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0. 0 0 20 30 40 50 60 70 80 90 00 n 23 5 2 2 2 9

2 0 02 7 S A P(A)= 24 n(a) n(s) 2 3 AB P(A)=;2!;P(B)=;3!;P(A;B)=;6!; P(A'B) P(A'B) =P(A)+P(B)-P(A;B) AB A p B q A B p_q 92

P(B A) P 4 7 2 0 2 24 8 42 2 P P (Bayes, T. ; 70~76) P(BA) n(a;b) = 2 n(a) A A;B U A B P S AP B n(s)=42n(a)=2n(b)=24 n(b) 24 =;4@2$;=;7$; n(s) n(a;b)=4 2 n(a;b) 24 =;2!$;=;3@; n(a) 0A A B A B P(B A) n(a;b) 24 n(a;b) n(s) P(A;B) P(B A)= 24 = 24 = 24 n(a) n(a) P(A) 24 n(s) 93

A B P(A;B) P(B A)= 24 (P(A)>0 ) P(A) P(A)=;4!;P(B)=;3@;P(A'B)=;4#; P(A B) P(B A C ) A B P(A)=;6#;P(A;B)=;6@; ;6@; P(A;B) P(B A)= = 4=;3@; P(A) ;6#; ;3@; 8 8 3 2 50 % 20 % A B P(A)=05P(A;B)=02 A B P(A;B) 0.2 P(B A)= = 25=;5@; P(A) 0.5 ;5@; 94

36 % 8 % 54 % 40 % 6% 46 % 76 % 24 % 00 % spam mail filtering 95

0ABP(A) P(B A) P(A;B) P(A;B) P(B A)= 24 P(A) P(A;B)=P(A)P(B A) P(A;B)=P(B)P(A B) AB P(A;B)=P(A)P(B A)=P(B)P(A B) (P(A)>0P(B)>0) 3 6 A B P(A;B)6 3 P(A)=;6#;P(B A) 3- P(B A)= 2 =;5@; 6- P(A;B) P(B A)= P(A;B)=P(A)P(B A) P(A) P(A;B)=;6#;_;5@;=;5!; ;5!; ;5!; 96

4 3 2 AB P(A)=;2!;P(B A)=;4!;P(A;B) P(A)=P(A B)=;6!;P(B)=;5@;P(B A) 2 0 3 ( ) ABCD 234 4 ABCD ABC D () 97

3 2 ;5#; ;4#; 0 AB P(B A)=P(B A C )=P(B) P(A B)=P(A B C )=P(A) AB AB AB A B P(B A)=P(B) P(A;B)=P(A)P(B A)=P(A)P(B) 98

P(A;B)=P(A)P(B) P(A;B) P(A)P(B) P(B A)= 24 = 24=P(B) P(A) P(A) P(B A)=P(B) AB AB P(A;B)=P(A)P(B) (P(A)>0P(B)>0) A 3 B AB S S={()(2)y(66)} n(s)=36 A 3 B n(a)=8n(b)=2 P(A)=;3!6*;=;2!;P(B)=;3!6@;=;3!; yy A;B={(23)(26)(43)(46)(63)(66)} P(A;B)=;6!; yy P(A;B)=P(A)P(B) AB A4 B2 5 C AB BC CA AB A C BA B C A C B C 0.60.8 AB 99

42 4 2 C =6 ;6!; ;6%; {;6!;} {;6%;} 2 3 4 5 :: :: :: 6 6 6 5 :: :: :: 6 6 6 5 5 :: :: :: 6 6 6 5 :: :: :: 6 6 6 5 5 :: :: :: 6 6 6 5 5 :: :: :: 6 6 6 5 :: 6 5 :: 6 :: 6 5 :: 6 :: 6 :: 6 C C {;6!;} {;6%;} =;2 6; A p n Ar nc r p r q n-r (q=-pr=02yn) 3 0.2 3 3 2 02 3 C (02) (08)=0096 0096 00

0 9 P y 3 6 x 2 A 6 y O P 2 3 x 5 O P A 20 20 4 A5 B AB 2 0 0.6 5 3 0 AB 0<P(A)<0<P(B)< AB A C B 0

. 0A A B A B 2. 0AB AB AB AB 3. 0 40 % 5 % 02 2 3 ( ) 03 ABC ;3@;;2!;;5@; 04 6 2 02

05 0.5 0.8 06 AB ( A+ZB+Z) AB 07 08 O P 2-2 - P O 2 3 P 03

NBC Lets make a deal (Monty Hall 92~) 990 9 ;3!; ;3@; 0 AB P(A B)= P(A)P(B A) P(B) 2 2 3 04

0 A A AB A;B=Z 02 500 350 03 6 5 3 AB P(A'B) =P(A)+P(B) 04 4 6 50 2 200 3 00 05 A B P(B A) 2 3 0 % 5 % 20 % 05

06 ABC AB BC P(A)=;2!;P(A'B)=;3@;P(B;C)=;8!; P(C) AB A;B=Z BC P(B;C)=P(B)P(C) 07 ;4!; AB P(A;B)=P(A)P(B) ;3!; 08 3 3 5 09 90 % 5% 20 % 06

n A n n 7 2 20 3 2 3 4 5 6 7 20 20 20 20 20 20 20 840 4 ;6!; 07

08

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