Tsu-2011 - ieeetsu

1 1 1 1
1
.
*
*
m m1
m 1
m1
saukeTeso obieqtis arCevis optimaluri strategia mdgomareobs ima-
Si, rom davakvirdeT da ukuvagdoT pirveli m * 1
obieqti da Semdeg gavagrZeloT
dakvirveba iseT * momentamde, roca pirvelad gamoCndeba yvela
winamorbedze ukeTes obieqti.
magaliTad, Tu m 1,..., 10, maSin m * -is Sesabamisi mniSvnelobebia:
m 1 2 3 4 5 6 7 8 9 10
m-optimaluri 1 1 1 1 2 2 2 3 3 4
sakmaod didi m-isaTvis m * m/
e (sadac e -- neperis ricxvia,
e 2.718 ) da saukeTeso obieqtis arCevis albaToba daaxloebiT tolia
1/ e 0.368 (Tumca, erTi SexedviT bunebrivia mogvCveneboda, rom gansaxilveli
obieqtebis m raodenobis zrdasTan erTad, saukeTeso obieqtis arCevis
albaToba unda wasuliyo nulisaken). e. i. saukeTeso obieqtis arCevis
optimaluri strategia mdgomareobs imaSi, rom unda ukuvagdoT obieqtebis
saerTo raodenobis daaxloebiT mesamedi da Semdeg avirCioT pirveli
iseTi obieqti, romelic yvela winaze ukeTesia.
magaliTi 3 (“bednier” bileTebze). 25 sagamocdo bileTidan 5 “bednieria”,
xolo danarCeni 20 – “ara bednieri”. romel students aqvs “bednieri”
bileTis aRebis meti albaToba: vinc pirveli iRebs bileTs, Tu vinc
meore iRebs bileTs?
amoxsna. es amocana Cven ukve amovxseniT albaTobis klasikuri ganmartebis
gamoyenebiT. amovxsnaT axla igi elementarul xdomilebaTa sivrcis
axleburi SemotaniTa da namravlis albaTobis formulis gamoyenebiT.
winaswar SemoviRoT Semdegi xdomilebebi: A iyos xdomileba, rom pirvelma
studentma aiRo bednieri bileTi, xolo B iyos xdomileba, rom
meore studentma aiRo bednieri bileTi. maSin cxadia, rom elementarul
xdomilebaTa sivrce Sedgeba oTxi xdomilebisagan
{ AB,
AB,
AB,
AB}
.
albaTobis klasikuri ganmartebis Tanaxmad P ( A)
5/ 25 1/
5, xolo
PA ( ) 20/25 4/5. meores mxriv, amocanis Sinaarsidan gamomdinare, Tu
cnobilia, rom pirvelma studentma aiRo bednieri bileTi, maSin albaToba
imisa rom meore studenti aiRebs bednier bileTs isev SeiZleba gamoviTvaloT
albaTobis klasikuri ganmartebiT: am SemTxvevaSi yvela SesaZlo
SedegTa raodenobaa 24, xolo xelSemwyob elementarul xdomilebaTa
raodenoba ki mxolod 4 (radgan erTi bednieri bileTi ukve aRebulia) da
Sesabamisad,
P ( B | A)
4/ 24 1/6.
analogiurad, P ( B | A)
20/24 5/ 6, P ( B|
A)
5/24 5/ 24 da
P( B| A) 19/24 . amitom ori xdomilebis namravlis albaTobis formulis
Tanaxmad gvaqvs:
P ( A
B)
P(
A)
P(
B | A)
1/51/6
1/30; P ( AB)
1/55/6
1/
6;
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