Combinatoria y Probabilidades
December 20, 2022 | Author: Anonymous | Category: N/A
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YPB@A@LCLDADG] Yrb`a`lcldad y Gstadësma
Leo. Fìmtbr Lváe Pbdrëougz Leo. Olsgcca Kaueb
1
KGTBDB] DG GEWKGPAMLBE Yara macmucar prb`a`lcldadgs sgrá egmgsarlb sa`gr mbkb mbeta`lclzar cas pbsl`lcldadgs dg bmurrgemla dg ue ngeýkgeb. Yara gccb rgvlsargkbs acouebs kìtbdbs dg geukgramlýe.
1) Yrlemlplb dg Kuctpclmamlýe ]upbeoa qug sg geg = kìtbdbs dg prbmgsaklgetb (A, @ y M) y tgkgebs 0 pbs dg prbdumtbs ,V g \. ²Muáetas kaegras fay dg mbk`lear kìtbdbs y prbdumtbs2
Dlaoraka dg ár`bc V \
(A V) (A \)
A p
V
@
\
M
V \
=
x
0
(@ V)
> nbrkas
(@ \) (M V) (M \)
; > 0
C0 ; e1 x e0
=
0) Yrlemlplb dg Adlmlýe ]upbeoa afbra qug gc kìtbdb M gs apclma`cg a ue tgrmgr prbdumtb X. ²Muáetas kaegras fay dg mbk`lear kìtbdbs y pgrsbeas2
Dlaoraka dg ár`bc
A p
@ M
V
(A V)
\
(A \)
V
(@ V)
\
(@ \)
V
(M V)
\ X
(M \)
0x0 ? nbrkas
+ 1x=
(M X)
?
4
7
AEACL]L] MBK@LEA TBPLB MBK@LEATBPLB Gc aeáclsls mbk`leatbrlb gstudla cas dlsetas aorupamlbegs qug sg pugdge nbrkar mbe cbs gcgkgetbs ge ue mbehuetb eltb.
• ^APLAMLBEG] • YGPKWTAMLBEG] •
MBK@LEAMLBEG]
>
YGPKWTAMLBEG] AMLBEG] YGPKWT Dgelmlýe8 ]l e gs ue getgrb pbslvb, dgelkbs e! ; ]be slkpcgkgetg cas varlamlbegs dg e b`hgtbs tbkadbs dg e ge e8 Dbs orupbs sg mbesldgr mbesldgrae ae dlsetbs, muaedb dlgrge ge gc rdge ge qug vae mbcbmadbs
E¹ dg Ygrkutamlbegs Namtbrlac dg e Ghgkpcb 18 pgrkutamlbegs pgrkutamlbegs dg dg 4 b`hgtbs8 b`hgtbs8 a,`,m,d ; 04
Ghgkpcb 08 ²Dg muaetas kaegras dlngr dlngrgetgs getgs pugdge sgetarsg 7 pgrsbeas ge uea kgsa2 Y ; 7! 7
Y7 ; 7.4.=.0.1
Y7 ; 109 kaegras dlset dlsetas. as.
?
MBK@LEAMLBEG] ]upbeoakbs qug tgegkbs 4 ledlvldubs
²Muaetbs orupbs dg dbs pugdb arkar mbe cbs muatrb2
4 , 0 ;
4 , 0
4!
0! ( 4 ∐0) !
()
;
4! ;
;
( )!
0! 0
4 , 0
4 ← ø 0
4 , 0
;
4.=.0 ! ;
0!0!
> 6
MBK@LEAMLBEG] ]g ccakae mbk`leamlbegs mbk`leamlbegs dg e b`hgtbs tbkadbs dg a k, b dg e ge k, a cbs dlsetbs orupbs qug sg pugdge nbrkar mbe gstbs b`hgtbs dg kbdb qug8 1. Ge mmad ada a orup orupb b getr getrae ae k dg dg cb cbss e b`hg b`hgtbs tbs
0. Dbs orupbs orupbs sg mbesldgr mbesldgrae ae dls dlstletbs tletbs muaed muaedb b dlnl dlnlgrge grge ge acouebs acouebs dg dg cbs b`hgtbs qug cbs brkae =. Eb lkpb lkpbrta rta gc b brd rdge, ge, sl q qug ug ccbs bs mbeh mbehuet uetb b dlnlgrae ge ac kge s ue gcgkget . E¹ dg mbk`leamlbegs dg e b`hgtbs tbkadbs dg k ge k8 Me,k , ;
!
! ( ∐ ) !
;
← ø
( )
<
^APLAMLBEG]
Tgegkbs 4 ledlvldubs
²Muaetbs orupbs dg dbs pugdb arkar mbe cbs muatrb2 Ygrb sl lkpbrta gc brdge
! , ; ( ∐) !
4 , 0
;
4!
( 4 ∐ 0 ) !
4 , 0
;
≩
10 19
^APLAMLBEG] Dadb ue mbehuetb eltb nbrkadb pbr e b`hgtbs a, `,m,…., f, j ccakakbs ^arlamlbegs dg cbs –e‛ b`hgtbs tbkadbs dg a –k‛ (slgedb k ≤ e), a cbs orupbs dg b`hgtbs qug sg pugdae brkar dg kbdb qug8
1) Ge mada orupb getrae k dg cbs e b`hgtbs 0) Dbs orupbs sg mbesldgrae dlstletbs, muaedb dlnlgrge ge acoue dg sus `hgt s, `lge (aue slgedb cbs klskbs b`hgtbs) ge gc rdge ge qug vae mbcbmadbs E¹ dg ^arlamlbegs dg e b`hgtbs tbkadbs dg k ge k ; ^e,k
!
, ;
( ∐) !
11
YPB@A@LCLDAD
Ca tardg dgc 14 dg huclb dg 0999 @aregy ^lesbe, gsmrltbr gspgmlaclzadb ge hugobs dg Masleb, sg gembetra`a ge gc Mìsar Yacamg dg Cas ^goas. Ge uea dg cas rucgtas gc ? saclý muatrb vgmgs sgouldas. @aregy mugeta qug qug gc hgng dg sgourldad dlhb a ue mbkpañgrb8 –Tg apugstb ue klccýe a qug eb sacg dg eugvb‛. Gc ? vbcvlý a saclr sgouldakgetg dbs vgmgs kás. ^lesbe nug tgsob dg acob qug sg fa rgolstradb sbcb ge dbs bmamlbaegs a cb carob dg ca flstbrla dgc hugob dg azar azar,, ca dg gsa tardg ge Cas ^goas, y ca dgc < dg huclb dg 17.?0>.49<
Ca sgmugemla 19,19,19,19,19,19 19,19,19,19,19,19 gs sbcb uea dg cas =?> qug fay, mbkb tbdas sbe louackgetg pbsl`cgs dg bmurrlr, getbemgs, ²muaetas huoadas gege qug rgaclzarsg rgaclzar sg para qug apargz apargza a ca sgmugemla kgemlbeada2 Ca nrgmugemla rgcava rgcava dg bmurrgemla gs dg 1/ =?> Cg ccakargkbs prb`a`lcldad ; 9,999999999=6
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