B4C3

3-, S ( ) a S A S {a} ( ) ( ) S A B AB A B AB A A A =S A A B AB= Ex.,,,3,4,5,6, () S AsS={,,3,4,5,6} () 4 A A AsA={,,3}A ={4,5,6} (3) B B AsB={,3,5}B ={,4,6} (4) C C AsC={,4,6}C ={,3,5} (5) 7 D D AsD= D ={,,3,4,5,6} (6) AB,A,B AsAB={,,3,5}AB={,3} (7) BC,B,C AsBC={,,3,4,5,6}BC= (8) CD,C,D AsCD={,4,6}CD= (9)S A As63 A B A,B Ex. S{,,3,4,5,6} A{,} ()S?()A As646 Ex3. 6 SA (S)(A) As00 4-3--/9

Ex4. 3 A B,C ()AAs{(,,),(,,),(,,),(,,)} ()BAs{(,,),(,,),(,,)} (3)CAs{(,,),(,,)} (4)A,B As{(,,),(,,),(,,),(,,),(,,)} (5)A,B As{(,,),(,,)} (6)A As{(,,),(,,),(,,),(,,)} (7)A,B As (8)B,C As Ex5. SA B ()(S)=As4 ()(AB)=As3 (3)(AB)=As5 (4)S ( S )=As 4 Ex6., S As79 Ex7. 0 5 () As: C 0 5 39 ()A 0 (A)=As C 0 C0 4-3--/9

3- Ex8. (Laplace) S A S A A ( A) ( A) P( A) = = ( S). () 3 4 5 6 7 8 9 0 3 4 5 6 5 4 3. () 3 3 4 5 6 7 8 9 0345678 3 6 0 5 5 7 7 5 5 0 6 3 () () 5(3) 5As 3 5 6 Ex9. 35 As 3 43 6 Ex0. () As4 () As3 (3) ( ) As4 (4) ( ) As3 (5) ( ) As (6) ( ) As Ex. 3 [88]As 5 4-3--3/9

Ex. As S AB S ()P( )=0P(S)=0P(A) () P(A )= P(A) (3) P(AB)=P(A)+P(B) P(AB) AB= P(AB)=P(A)+P(B) (4) A B P(A)P(B) (5) ABC S ABC P(A B C)=P(A)+P(B)+P(C) P(A B) P(B C) P(C A)+P(A B C) (6) P(A B)=P(A B )=P(A) P(A B) Ex3. 70 50 68 69 70 7 7 5 5 0 5 5 7 [88]As 9 5 Ex4. A B 3 p A B p 5 5 () p () < p (3) < p < (4) p (5) p > [87]As4 6 6 3 3 6 6 Ex5. 6 (6 ) [87]As 5 9 Ex6. 7 ( ) [86] As 6 35 Ex7. 3...0 [85]As 5 4-3--4/9

Ex8. 0 0 4 4 3 7 [84]As 4 Ex9. 4 5 9 [8]As 33 Ex0. 0 0 4 6 4 4 [8]As 3 Ex. 09 3 3 () 0 () 0 9 [80]As0.70.054 Ex. ()3 ()34 [77]As 5 Ex3. 34 56 7 [76]As 7 Ex4. 0 99 00 3 () () [76] As 6700 73 8085 Ex5. 5 5 36 [73] As 78 4-3--5/9

.A S P(A)>0B S A P B P(B A) P(B A)= ( A B ) PA ( ) P. P(B A)= ( A B ) A ( B) = PA ( ) A ( ) 3. ABC S P(C)>0 ()P( C)=0 ()P(C C)= (3)0 P(A C) (4)P(A C)= P(A C) (5)P(AB C)=P(A C)+P(B C) P(AB C) (6)A B P(A C) P(B C) 4. ()P(AB)=P(A)P(B A) ()P(ABC)=P(A)P(B A)P(C AB) (3)P(A A...A )=P(A )P(A A )...P(A A A...A - ) Ex6. 0 3 () () As 3 0 3 0 3 0 3 0 Ex7. 3456 ( 4 6 ) 5 [89]As 7 8 Ex8. [87]As 3 7 Ex9. 4 [86]As 46 9. (Partitio) A A A r S ()A A A r =S ()A i A j = i jij=r {A A A r } S 4-3--6/9

Ex30. 600 400 36 46 [90]As40% Ex3. 0.9 0.04 0% [79]As0.6.{A A A r } S B P(B)>0 ()P(B)=P(B A )+P(B A )+ +P(B A ) =P(A ) P(B A )+P(A ) P(B A )++P(A ) P(B A ) = = P( A )( B A ) P( A B) j ()P(A j B)= = PB ( ) PA ( ) PB ( A) j j = P( A ) P( B A ) ( ) (3) P(B) P(A j B) 5 ( ) 96 Ex3. 0.0 0.6 5 95 As 96 As 6 A A A 3 A B Ex33. 0.8 5 ( ) [89]As 0 4-3--7/9

Ex34. A B 30%70%A % B 5% (A) A (B) B (C) A 3/38 (D) A 30/0000 (E) B 350/0000[85]AsBC. AB S () P(A B)=P(A) P(B) AB () AB A B A B A B. ABC ABC S () ABC P(A B C)=P(A) P(B) P(C) P(A B)=P(A) P(B) P(B C)=P(B) P(C) P(C A)=P(C) P(A) P(A B C)=P(A) P(B) P(C) S={,,}A={,4,6,8,0,}B={3,6,9,}C={,5,6,7,,} () ABC ABC AB C A BC AB C A BC A B C A B C 3. p () p () ( p) ( p) (3) C p ( p) =3 Ex35. 0. 0. [86]As0.83 Ex36. 5 5 ( ) = 40 3 5 p (A)0.4 p<0.5(b)0.5 p<0.6(c)0.6 p<0.7(d)0.7 p<0.8(e)0.8 p<0.9 log3=.494log3=.505log.83=0.45[86]asd 4-3--8/9

Ex37. 0.4 0.5 [84]As0.30.6 Ex38. 3 [83]As 30 Ex39. 4 5 ( ) () As 40 63 3 63 () As 9 4 Ex40. P(A)=aP(B)=bP(AB)=c abc () P( A B ) =As c () P( A B) =Asb c (3) P( A B) =As a+c (4) P( A B ) =As a b+c Ex4. () 5 () As 6 Ex4. 3 abc ()a<b<c()abc (3)a+b+c=(4)(a-b)(b-c)=0(5)(a-b)(b-c)=As 5 54 7 8 36 8 7 Ex43. As 5 96 Ex44. () 0 3 5 5 () 4 AsC 9 ( ) 3 ( ) 7 3 ( )( ) 6 6 6 6 Ex45. () 6 () (3) As 9 6 5 9 7 36 4-3--9/9

Ex46. A P(A)>99.8% (log=0.300log3=0.477)as35 Ex47. A B Ax + By = 3 As x + y = Ex48. a b f(x)=3x +ax+b 3 As 3 Ex49. f(x)=x +ax+b ab ()f(x)=0 As 9 36 ()f(x)=0 As 7 36 (3)f(x)=0 As 7 36 (4) x f(x) As 7 36 Ex50. 3633 6 () () (3) 3 (4) 4 (5) 5 (6) 8 As348 36 5 7 44 6 Ex5. 0.999 As0 Ex5. 5 () () 50 0 As 7 8 Ex53. 4 5 5 4 As 4 65 4-3--0/9

Ex54. 3 P(A) P(B) A B As 3 0 3 5 As 9 5 5 Ex55. 5 4 3 4 () 6 73 () As 65 Ex56. 3 (3 ) 5 (345 ) 6 (3456 ) 4 9 () () (3) As 3 9 3 Ex57. 00 3 As0.33 Ex58. 345 3 () () 4 As 5 5 Ex59. 3.00 As 66 Ex60. 5 () () (3) (4) (AKQ J)As 7 4 7 3 7 3 Ex6. 3 3 0 0 3 As 583 4-3--/9

3 Ex6. ABC p( B) = p ( C) = 5 3 p ( A B ) = p ( B C) = p ( C A) = p ( A B C) = 5 0 5 0 9 p( A B C) = ()p(abc )=()p(a)=as 0 0 3 5 Ex63. ABC P(A)=P(B)=P(C)=0.P(A B)=0. P(B C)=P(C A)=0 As0.5 Ex64. AB P(A B)= 3 4 P(A )= 3 P(A B)= 4 ()P(A)()P(B)(3)P(A B)As 3 3 Ex65. AB P(A)=0.P(B)=0.4 P(A )P(A B ) As0.80. Ex66. AB P(A B)=0.3P(A B )=0.5 P(A)P(B) As0.0.3 Ex67. 3 4 () () As 05 35 3 Ex68. 5 4 As Ex69. 0 4 As 4 33 3 33 99 33 Ex70. 3 4 4 As 53 05 Ex7. ( ) 3 4 5 0 0 5 7 As 8 8 8 7 8 4-3--/9

Ex7. ABCDE () () 4 (3) 3 (4) (5) (6) 3 As 0 6 8 30 0 Ex73. 4 () () (3) As 5 8 3 8 3 Ex74. 0 A 4 B 3 C 3 () A () As 5 4 5 Ex75. AB As 8 Ex76. 0 As 0 8 Ex77. As Ex78. As 35 Ex79. ax +bx+c=0 abc { } As Ex80. 046 As 3 4-3--3/9

3-3 E. p m p m. S{A A...A } S A i p i i=3... A i m i i=3... p m =pm +p m +---+p m = Ex8. 4 5 As 4 Ex8. 3- (=3) 7 5 As 4 Ex83. 7 00 7 00 As0 Ex84. 345678 876543 As 0 3 3. 4. E E Ex85. As 7 735 Ex86. As 49 4 35 8 4-3-3-4/9

Ex87. 0 5 4 4 As 5 As 44 5 As 44 5 Ex88.... + As 3 5. Ex89. 0 As 60 50 Ex90. 64 As 44 0 6. =0 Ex9. 00 As0 Ex9. ( /) 50 0 40 30 5 30 0 0 30 0 5 P =0.3 P =0. P 3 =0.4 P 4 =0. ( )[89]AsE()=E()=7E()=.6 4-3-3-5/9

Ex93. 0 9 90 900 [88]As 63 0 Ex94. 5 [85]As 9 Ex95. 3 3 3 () ()3 (3) 8 [8]As 9 9 9 Ex96....5 5 (00 ) 9 [80]As 9 35 83 Ex97. 6 3 ( ) [86]As 7 6 Ex98. 3 5 [88]As 4 3 Ex99. 5 As Ex00. 0 5 3 As5 Ex0. 0 3 00 50 5 0 As45 Ex0. 9 4 3 As 4 3 4-3-3-6/9

Ex03. 345 As9 Ex04. 0.75 0 5 As75 Ex05. () 00 500 () 50 0 As 5 3 50 3 Ex06. As 3 6 Ex07. 3 4 As 5 8 Ex08. 5 3 () 0 30 40 () 90 As78 Ex09. 0...9 4 4 4 000 3 50 5 As 65 Ex0. 3 4 As6 Ex. 6 3 3 Ex. 5 4 0 0 As 65 9 3 9 4-3-3-7/9

Ex3. 59 00000 50 59 60 0.997 As0 3 Ex4. ABC,, 48 4 3 As46 Ex5. ( ) a + b(a>b) a b As 3 Ex6. 9 9 9 4 As Ex7. 3 4 0. 0.43 0.34 0. As 3 0 Ex8. 0 00 0 50 As 0 Ex9. 3 5600 3 5600 As 4900 700 Ex0. 000 5 0 00 As00 Ex. () 8 () ( ) 6 As 5 4-3-3-8/9

3-4 ( ).. 3. 4. 5.... () ( ) () ( ). N N = N ()N=+c0<c< c () N (N+) ( r )r r+r+...r+(-) 3. 4. ( ) Ex. 0 5 6 [89]As00 4-3-4-9/9

Ex3. 3 49 35 4 7 ( ) As 7 Ex4. () As () As (3) As (4) As Ex5. 30 0 5 3 74787569 64 647055 As68.4cm 98 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 0 0 6640 50 83 76 66 80 45 90 83 7 60 68 73 74 5 9 84 7 6 54 40 979 839 Ex6. 0 5 () 085 0 5 ( ) 0 () 4 3 ( 458 ) 393 (3) 60 60 80 80 55 63 34 0 45 0 0 4 563 35 Ny + N y + N3 y3 y =, N + N + N3 = N 999 N 75 N i i yi i 607 y = ( ) (4) ~56~0~56~0 ~5 ( ) (5) As73.7666.757.868.7 Ex7. 3 4 0 As7 4-3-4-0/9

3-5 () () ( ) ( ) () (). =. 5~5 3. = 4. ( ) ( ) 5. 6. 7. 8. () () () () (3) L ~U f f f +f ++f L ~U f f +f f ++f L ~U f f +f ++f f (4) Ex8. 50 30 5 0 () 5 () 0 (3) 5 As.764%80 0 0 4-3-5-/9

Ex9. ()60 () 70 (3) 80 ~90 As807 Ex30. 5 ( ) 35~38 38~4 4~44 3 44~47 8 47~50 7 50~53 3 53~56 4-3-5-/9

3-6 M(Mea)X. ( ) M = ( x + x + + x ) = x i i= Ex3. 30 75 35 7 35 80 As75.7. ( ) M = ( fx + f x + + f x ) = f i xi i= () M = fi xi = fi[ A + ( xi A)] = A + i= i= i= f ( x x () i A h M = fixi = fi[ A+ h )] = A+ h i= i= i i A) i= xi A fi ( ) h Ex3. 0 =As68 4050 5060 6070 7080 8090 3 6 5 4 Ex33. 0,, ( ) =As75 3. () () i= ( x M) = 0 i 50~55 55~60 60~65 65~70 70~75 75~80 80~85 85~90 4 0 4 30 30 8 ( xi M) ( xi p) i= i= p (3) X + a = X + a, bx = bx, bx + a = bx + a (4) ( y )M( ) W x x x w w w w x + wx + + w x W = w + w + + w Ex34. 6 6 6549757380 3445 As 75 4-3-6-3/9

G.M. x x x G. M. = x x SMAMGMHM( ) Ex35. 34897 As6 x Ex36. 990 0 000 0 ( log=0.300log.07=0.030)as7.% Me(Media). ( ) ( ) M L f f e i. i = i M = L + ( U L ) U L f e i f i i i i i 3. Ex37. 0 =As68.33 i 4050 5060 6070 7080 8090 3 6 5 4 Ex38. 0,, ( ) =As76.33 50~55 55~60 60~65 65~70 70~75 75~80 80~85 85~90 4 0 4 30 30 8 Mo ( fi fi ) 3 M o = Li + ( Ui Li) ( f f ) ( f f ) i i i+ i Ex39. 0 385037444646384 4640 As4.74346 Ex40. 00 3 4 5 6 a b a b=[77]as0.4 0 5 0 0 0 5 4-3-6-4/9

Ex4. 00 ( ( ( ( ( = =[83] ( ( As64.564 Ex4. 50 ( ) (A) (B) (C) 85 (D) (E) [89]AsACDE Ex43. ( ) (A) 0 (B) 00 (C)5060 8 (D) 7080 (E) 60 70 [8]AsADE 0-0 0-0 0-30 30-40 40-50 50-60 60-70 70-80 80-90 90-00 0 3 4 7 8 4-3-6-5/9

3-7 (R) (Q.D.) (σs) (R) MAX MIN ( ) Q.D.=Q 3 Q ( ) Q ( ) 3 Q 3 3 Q Q 3 4 4 Q Q 3 (Me) () Q 4 4 () [ ] Q 4 4 (3)Q 3 = = = σ + M = ( ) S + M. (σ) σ = ( x M) = x i i M i= i= σ = f ( x M) = h f d M i i i i M x i i = = ( i= i= ) xi A d i = ( )M h Ex44. 80 68,80,80,80,86 [86]As6 Ex45. 48, 70 σ 80 50 70 00 σ σ σ [89] (A)σ <σ 5(B)σ 5 σ <σ(c)σ =σ(d)σ<σ σ+5(e)σ+5<σ AsB Ex46. 00 7 4 00 77 5 300 [79]As735. 4-3-7-6/9

Ex47. 0 56 4 0 8 50,5,53,54,56,57,60,6 As5463. (S) S ( ) ( ) ( ) ( x M i x M i x M = = = = σ i i= i= i= S = f ( x M) = h ( f d i i i i i= i= = h f d M ( ) i i i = M ) ( )M Ex48., 8 ( ), 67,58,6,75,70,8,64,66( ), RQ.D.MS As49.56858 ) Ex49. As645.8 0-30 30-40 40-50 50-60 60-70 70-80 80-90 90-00 7 9 3 0 6 Ex50. 3 56 4 6 30 As55.83.9 3. = 4. =0 5. 6. Ex5. 9,8,,4,0,8,7,0,3,0 RMQ.D. As4505.04 Ex5. 9,8,,4,0,8,7,0,3,0 RM Q.D. As4050050.4 Ex53. x =6S x =4 x=4y 3 y As 9 4 4-3-7-7/9

Ex54. x, x,, 60 40 45 x 6 3 3x+ 3x + 3x 3 + 3x + RMMeQ.D.SAs80 8 3389 Ex55. 9 ( ).43,.46,.4,.45,.44,.48,.46,.47,.45 00 40 3,6,,5,4,8,6,7,5? (A) 5(B) (C).45(D) 0. (E).45[88]AsABCE (M+,M ) 68.6% (M+,M ) 95.44% (M+3,M 3) 99.73% M 3σ M σ M σ M M + σ M + σ M + 3σ Ex56. 000 70 0 ()?() 90?(3) 80?As60560 Ex57.,,3,, As Ex58. 5 ( 0 ) A,,,,,0,0,0,0,0 B,,,,,5,5,5,5,5 C4,4,4,5,5,5,5,6,6,6 D,,,,3,3,4,4,5,5 E,,3,4,5,6,7,8,9,0 [89]AsA Ex59. 30 0 70 60 0 8 As660.4 Ex60. 0 A,B A 6 3 9 B 4 8 4 A,B As57 4-3-7-8/9

30( X X ) Ex6. X X S Y = + 70 S () Y Y As70 () Y S Y As30 Ex6., 5 ( ),, (A) (B) (C) (D) (E) [88]AsCE Ex63. 30,40,60,50,70,80,60,90,60 0 7 () As60 3 () () 60? As64 () 60? As46 (3) 70 60?[84]As 3 7 4-3-7-9/9