sh-m2010
Dieses Dokument ist Teil der Anfrage „Mathe-Abiturprüfung (BG)“
! " "!
D" B ! Φ
Φ<− ; Φ< ; Φ<− ; Φ< ; Φ<− ; Φ< ; Φ<− ; Φ< ;
4 4 4 4 4 4 4 4
4* 8>E 7C*> 4 7EE= 4C = 77 4= 8 77E8
4* 8 * 7CEC 4 E 7E=> 4C E= 77 4= C 77E*
4*> 8 * 7C=C 4 > 7E== 4C> E8 77 8 4=> > 77EE
4*C 8 8 7C78 4 C E 7E7> 4CC E> 77 E 4=C > 77EE
4*8 C78 78 8 4 8 7E7= 4C8 E 77 7 4=8 77E=
4** C=8 78 8 4 * 7E 7= > 4C* *7 77> 4=* 77E7
4*E CE8 78 8 4 E 7 7= = 4CE *= 77> 4=E 77E7
4*= C*8 78>8 4 = == 7= 4C= ** 77>C 4== 77=
4*7 C88 78C8 4 7 => 7= E 4C7 *C 77>* 4=7 7 77=
4E CC* 788C 4 E7 7= (&% * 77>= 47 7 77=
4E C>* 78*C 4 EC 7= * 48 * 77C 47 = 77=
4E C E 78E> 4 E 7=> 48 87 77C 47 = 77=
4E> C = 78= 4 > ** 7=>C 48> 8E 77C> 47> E 77=>
4EC C 7 787 4 C * 7=>= 48C 88 77C8 47C * 77=C
4E8 C 7877 4 8 8= 7=C 488 8C 77C* 478 * 77=C
4E* >7 7* = 4 * 8C 7=C* 48* 8 77C= 47* 8 77=8
4EE >=C 7* * 4 E 8 7=8 48E 8 77C7 47E 8 77=8
4E= >E8 7* 8 4 = C* 7=8C 48= C7 778 47= C 77=*
4E7 >*E 7*>> 4 7 C> 7=8E 487 C= 778 477 C 77=*
4= >87 7*C 4 >7 7=* 4* CE 778> )&%% > 77=E
4= >8 7*C7 4 >* 7=*C 4* C8 7788
4= >CC 7*8* 4 > 7=*= 4* CC 778*
4=> >>* 7**C 4 > 7 7=E 4*> C> 778E
4=C > 7 7*E 4 C 8 7=E8 4*C C 7787
4=8 > 7*E= 4 8 7=E= 4*8 C 77*
4=* > C 7*=* 4 * 7 7== 4** >7 77*
4=E > E 7*7> 4 E * 7==C 4*E >= 77*
4== > 7*77 4 = > 7==E 4*= >E 77*>
4=7 7C 7E * 4 7 7=7 4*7 >* 77*C
47 =E 7E > 4> E 7=7> 4E >8 77*8
47 = 7E 7 4> C 7=7* 4E >C 77**
47 EC 7E * 4> 7=7= 4E >> 77*E
47> *= 7E> 4>> 77 77 4E> > 77*=
47C * 7E>= 4>C 7* 77 C 4EC > 77*7
478 8* 7ECC 4>8 7C 77 * 4E8 > 77E
47* 8 7E8 4>* 7 77 7 4E* 7 77E
47E CC 7E8* 4>E =7 77 4EE = 77E
47= >7 7E* 4>= =E 77 > 4E= E 77E>
477 >> 7E*E 4>7 =C 77 * 4E7 * 77EC
(&%% = 7EE 4C = 77 = 4= * 77EC
Seite 4 von 7
2010_M_H5_Stochastik_L.doc nur für Lehrkräfte
! " "!
F
! $ *
2 22 222
"; , !1 " ,4 " '" 4
" ,4 " " , ) 5 4
4 " " , ) 5 +
,
< ; = 4 4
< ; = 478
< ; = 47 G "
< ;
= < ; ⋅ < ; + < ; ⋅ < ; ⋅ < ; + < ; ⋅ < ; ⋅ < ;
= 4 ⋅ 4 8 + 4 ⋅ 478 ⋅ 4 8 + 47 ⋅ 4 ⋅ 4 = 4 =E8+ >
< ;
, !1 " ,4 " ) "
" ) 5 " " +
< ∩ ;
< ; =
< ;
< ; ⋅ < ; ⋅ < ;
=
< ; ⋅ < ; ⋅ < ; + < ; ⋅ < ; ⋅ < ;
47 ⋅ ⋅ 4
=
4 ⋅ 478 ⋅ 478 + 47 ⋅ 4 ⋅ 4
4 7
= ≈ 74 E9
4 7 8 + 4 7 C
< ;
; ! 1" A "@
) + <! 6 "+;
'" 1 $ ?)
""@ " 6"!
− < − ; 1 ,1 + / 1 "
1" ) ," 5 !
+
Es gilt < ! ; = ⋅ < − ; + ⋅ < − < − ; ; .
Seite 5 von 7
2010_M_H5_Stochastik_L.doc nur für Lehrkräfte
! " "!
/ ," D" 1"
1 "@ " < ! ; + +
F "4 6 < ! ; +
! " +
+ ⋅ < − < − ; ; + <
7
− < − ; <
< − ; > 4
− >
4
< − 4 ≈ − 4E7C> = 48E9
! " 4 8E " "@ C
" !" -+
; / F "AB ! A 1"
'"4 " "+
! @ 5 )"" " H * 4
# H H *+
< $ % &' %
'( ) $% ;
§ · § C= ·
¨ ¸¨ ¸
*
< ! ≥ ; = − < ! = ; = − © ¹ © ¹ ≈ − 4 C8 = E84 C79
§ * ·
¨ ¸
© * ¹
2 ' * A 1"
DA '"4 " 1 !
! +
* @ 5 )"" " H * 4
# H * H *+
§ * · § 8C · § * · § 8C ·
¨ ¸¨ ¸ ¨ ¸¨ ¸
* © ¹ © 8 ¹
< ! ≤ ; = < ! = ; + < ! = ; = © ¹ © ¹ +
§ * · § * ·
¨ ¸ ¨ ¸
© * ¹ © * ¹
≈ =74 C79
Seite 6 von 7
2010_M_H5_Stochastik_L.doc nur für Lehrkräfte
! " "!
! @ 5
!" )"" +
§ C= ·
¨¨ ¸¸
, < ! = ; = © ¹ + ' H * " <! = ; ≈ C + 8 ,
§ * ·
¨¨ ¸¸
© ¹
/ 6"! <! = ; AB4 # !
$ +
@ " ) I
8 C >
<! = ; 4> >8 4>77 48 8
, " A > " C
* / +
-( . / %
% + 0
; / 6"!4 "
) " 5$ 4 789+
/ "B ) ! 6"!
:" 5 478J 478 H 7 4 89+
/" ! 6"! :$ +
/ '"4 " /
4 $4 "
&" ( +
' $ !"" "4 " % 1 3
$ + / - 4 "
6"! 94 "
/ 1 4 +
) ! 6"! " 4 J 4 H 9+
/" &(
- A+ >
<% / 1% ;
8 >
Seite 7 von 7
2010_M_H5_Stochastik_L.doc nur für Lehrkräfte
! " "!
!"
#$ !
# " $ """
" % & ' "
" (" ) ) *) +) # , -.
. /01) . / 1) *. 21) +. 1) #. 01) . 1 3
% 4 $ " "$ " ) " 5 6
" " ( 6 7" 3
"8 +" ' " $ ") " ! "
,%- "6 ") *"* " ")
" 9 " 6 "3 : " *"
* ; $) 6 < "< 6
( "3 % "$ " )
" " (" ! ! "
" ( " <& (" ")
6 < !3
• 7"!
# = >"!.
# . ,%" /01 ; 6 " (
(" "3-
# . , 6 7< ("
"3-
• 7"! #
5 ?< $ " $
@ # 3 A (8
8 +" 01 " 7"
"" " B (" ") " (" #
7!" " "3 B #"6
% = (" # ) " "
"3 +"6 " " (" @
+ !"63
#! " @ 9$ " "
$ 0 ( !"6$" $ 213 %
"6 # "3 AC (8
2010_M_H6_Stochastik_L.doc nur für Lehrkräfte Seite 1 von 8
! " "!
8 9 " " <& 201
,6 <- " ( " 6
< & 3
6" $ ( ) "
@ " )
7"! $ " C01 0 $
6 < & 6 3 A; (8
8 # ( 6 7"$" "3 +
7"!) " " ( "
7< (" 6 ! ) " 3
) " " ("
' ≥ − − 3 A/ (8
2010_M_H6_Stochastik_L.doc nur für Lehrkräfte Seite 2 von 8
! " "!
%" & ! Φ
ΦA− 8 ΦA 8 ΦA− 8 ΦA 8 ΦA− 8 ΦA 8 ΦA− 8 ΦA 8
) ) ) ) ) ) ) )
) DCE 0 D )D /D C E0C ); C 2C ) / ;;EC
) DC 0 ; )D //2 EE ; ); E 2C/C ) ;;;;
) / D;; 0 )D/ ///E EEED );/ // 2CE2 ) / C/ ;C 2
) D D;D 0 E )DD // E2 );D 0 2CC0 ) D 20 ;C 0
) 0 D; 0 CC )D0 / ED E2/E );0 C22 ; / ) 0 0E ;CDD
) E D2E 0 /C )DE / ; E22 );E CDC ; 0 ) E /; ;CE
) 2 D2 0 2C )D2 / C E; ; );2 C ; 2; ) 2 ;C;
) ; DE; 0/ C )D; / 0E E;DD );; ;CD ; E ) ; / ;CC2
) C DED 0/0C )DC / E;2C );C ;E2 ; // ) C C;0 C 0
) DE 0/C; %&'% / ;0 EC 0 )C ;D ; 0C )/ CE; C /
) D0E 0D/; )0 / 0 EC0 )C ; D ; ;E )/ C0 C DC
) D0 0D2; )0 / 0 EC;0 )C 2;; ; )/ C/D C EE
) / DD;/ 00 2 )0/ C; 2 C )C/ 2E ; /; )// C ; C ;
) D DDD/ 0002 )0D CDE 2 0D )CD 2/E ; ED )/D C C CC
) 0 DD D 00CE )00 C 2 ;; )C0 2 ; ;C )/0 ;;0 C 0
) E D/ED 0E/E )0E ;22 2 / )CE E;0 ;/ 0 )/E ;EC C /
) 2 D/ 0 0E20 )02 ;D/ 2 02 )C2 EE ;/D )/2 ;0/ C D2
) ; D ;E 02 D )0; ; 2 C )C; E/0 ;/E0 )/; ;/; C E
) C D D2 020/ )0C 22E 2 D )CC E ;/;C )/C ; / C 22
) D 2 02C/ )E 2D/ 2 02 (&%% 0;2 ;D / )D ; ; C C
) D E; 0;/ )E 2 C 2 C ) 0E ;D/; )D 2C/ C 2
) D C 0;2 )E E2E 2/ D ) 0/C ;DE )D 22; C
) / D C 0C )E/ ED/ 2/02 ) / 0 0 ;D;0 )D/ 2ED C /E
) D D 0 0CD; )ED E 2/;C ) D DC ;0 ; )DD 2DC C 0
) 0 D / 0C;2 )E0 02; 2D ) 0 DEC ;0/ )D0 2/0 C E0
) E /C2D E E )EE 0DE 2D0D ) E DDE ;00D )DE 2 C 2C
) 2 /C/E E ED )E2 0 D 2D;E ) 2 D / ;022 )D2 2 ; C C
) ; /;C2 E / )E; D;/ 20 2 ) ; D ;0CC )D; ECD C/ E
) C /;0C E D )EC D0 20DC ) C /2C ;E )DC E; C/ C
)/ /; E 2C )2 D 20; ) /02 ;ED/ (&'% EE; C//
)/ /2;/ E 2 )2 /;C 2E ) //0 ;EE0 )0 E00 C/D0
)/ /2D0 E 00 )2 /0; 2ED ) / D ;E;E )0 ED/ C/02
)// /2 2 E C/ )2/ / 2 2E2/ ) / C ;2 ; )0/ E/ C/2
)/D /EEC E// )2D CE 22 D ) D 2 ;2 C )0D E ; C/;
)/0 /E/ E/E; )20 EE 22/D ) 0 0 ;2DC )00 E E C/CD
)/E /0CD ED E )2E /E 22ED ) E / ;22 )0E 0CD CD E
)/2 /002 EDD/ )22 E 22CD ) 2 ;2C )02 0; CD ;
)/; /0 ED; )2; 22 2; / ) ; C ;; )0; 02 CD C
)/C /D;/ E0 2 )2C D; 2;0 ) C 2 ;;/ )0C 00C CDD
)D /DDE E00D ); C 2;; ) 0 ;;DC )E 0D; CD0
2010_M_H6_Stochastik_L.doc nur für Lehrkräfte Seite 3 von 8
! " "!
%" & ! Φ
ΦA− 8 ΦA 8 ΦA− 8 ΦA 8 ΦA− 8 ΦA 8 ΦA− 8 ΦA 8
) ) ) ) ) ) ) )
)E 0/2 CDE/ ) C22; )D ; CC ); 0 CC20
)E 0 E CD2D ) 2 C2;/ )D 2; CC ); D CC2E
)E/ 0 E CD;D ) / C2;; )D/ 20 CC 0 );/ / CC22
)ED 0 0 CDC0 ) D 2 C2C/ )DD 2/ CC 2 );D / CC22
)E0 DC0 C0 0 ) 0 C2C; )D0 2 CC C );0 CC2;
)EE D;0 C0 0 ) E C2 C; / )DE EC CC/ );E CC2C
)E2 D20 C0 0 ) 2 C C; ; )D2 E; CC/ );2 CC2C
)E; DE0 C0/0 ) ; ;; C; )D; EE CC/D );; CC;
)EC D00 C0D0 ) C ;/ C; 2 )DC ED CC/E );C C CC;
)2 DDE C00D ) 2C C; )&'% E CC/; )C C CC;
)2 D/E C0ED ) 2D C; E )0 E CCD )C ; CC;
)2 D 2 C02/ ) 2 C;/ )0 0C CCD )C ; CC;
)2/ D ; C0; ) / EE C;/D )0/ 02 CCD/ )C/ 2 CC;/
)2D D C C0C ) D E C;/; )0D 00 CCD0 )CD E CC;D
)20 D C0CC ) 0 0; C;D )00 0D CCDE )C0 E CC;D
)2E /C CE ; ) E 0D C;DE )0E 0 CCD; )CE 0 CC;0
)22 /;D CE E ) 2 0 C;0 )02 0 CCDC )C2 0 CC;0
)2; /20 CE 0 ) ; DE C;0D )0; DC CC0 )C; D CC;E
)2C /E2 CE// ) C D/ C;02 )0C D; CC0 )CC D CC;E
); /0C CED ) /C C;E )E D2 CC0/ *&%% / CC;2
); /0 CEDC ) /E C;ED )E D0 CC00
); /DD CE0E ) / C;E; )E DD CC0E
);/ //E CEED ) / C C;2 )E/ D/ CC02
);D / C CE2 ) D 0 C;20 )ED D CC0C
);0 / CE2; ) 0 C;2; )E0 D CCE
);E / D CE;E ) E C C;; )EE /C CCE
);2 / 2 CEC/ ) 2 E C;;D )E2 /; CCE
);; / CECC ) ; / C;;2 )E; /2 CCE/
);C CD C2 E ) C C;C )EC /E CCED
)C ;2 C2 / )/ 2 C;C/ )2 /0 CCE0
)C ; C2 C )/ D C;CE )2 /D CCEE
)C 2D C2 E )/ C;C; )2 // CCE2
)C/ E; C2/ )// CC CC )2/ / CCE;
)CD E C2/; )/D CE CC D )2D / CCEC
)C0 0E C2DD )/0 CD CC E )20 / CC2
)CE 0 C20 )/E C CC C )2E C CC2
)C2 DD C20E )/2 ;C CC )22 ; CC2
)C; /C C2E )/; ;2 CC / )2; 2 CC2/
)CC // C2E2 )/C ;D CC E )2C E CC2D
)&%% ; C22 )D ; CC ; ); E CC2D
2010_M_H6_Stochastik_L.doc nur für Lehrkräfte Seite 4 von 8
! " "!
F
$ +
@ @@ @@@
"8 6" 7< (" 3
"$ ("" = ; ) = )/0 3
§ ; ·
A = ;8 = ¨ ¸ ⋅ )/0 ; ⋅ )E00 ≈ ) C/ 3
© ; ¹
+ 7"!) " $ ; " ( "
/01 (" ") C)/13
6" 7< ("3
"$ ("" = ; ) = ) 3
A ≥ 8 = − A = 8 − A = 8
§ ; · § ; ·
= − ¨ ¸ ) ⋅ )C;2C − ¨ ¸ ) ⋅ )C;;
© ¹ © ¹
≈ − )/ D/ − ) C;E = ) D22
+ 7"!) " 6 7< "
(" " ) D2)213
?< ? "$
F "$"" " ) " ""
⋅ ⋅ A − 8 = ; ⋅ )/0 ⋅ )E0 = ;) > C 3
A "8 ?<
§ ;)0 − ; · § 2)0 − ; ·
A = ;8 ≈ Φ ¨ ¸ − Φ¨ ¸
¨ ;) ¸¹ ¨ ;) ¸¹
© ©
≈ ΦA ) 8 − ΦA− ) 8 ≈ ⋅ )0D2; − = ) C0E 3
+ ?< 3"3 73
A
) C/0 8
2010_M_H6_Stochastik_L.doc nur für Lehrkräfte Seite 5 von 8
! " "!
A ! "
# $ %&
⋅ ⋅ A − 8 = ; ⋅ ) ⋅ )C; = )0E; < C 8
" " 7"! $ 1 " @6
, #- " " 6" G ;
" &) !" " ( $ "
?< $3 A' & ( 8
A ≥ 8 = − A = 8 − A = 8
)E )E
≈ − − )E ⋅ − − )E ⋅ ≈ ) D20 3
H H
+ ?< 3"3 73
8 +" F 9 01
(" #3 +"6 %I 6
" 63 + A"6 8 ? I " "
) . ≤ ) 0 3
+ F "$"" 6" 7<
(" #3
" $ ) "$
("" = 0 A "8
"> " 7"! = ) 0 3
" I ") F" 7<
$ # "$ & ) "
J + K333K 0 L 3
+ ""
⋅ ⋅ A − 8 = 0 ⋅ ) 0 ⋅ )C0 = 2 ) 0 > C ) " !"
? "$ " ?< $ 3
% !"6$" $ 21 "
4 .
A ≥ + 8 ≤ ) 2 63 A ≤ 8 ≥ )C/ 3
§ + )0 − 20 ·
A ≤ 8 ≈ Φ ¨ ¸ ≥ )C/
¨ 2 ) 0 ¸¹
©
+ )0 − 20
≥ ) D;
2 ) 0
2010_M_H6_Stochastik_L.doc nur für Lehrkräfte Seite 6 von 8
