Tsu-2011 - ieeetsu

amdenadac 365, Tu visargeblebT niutonis binomis formuliT
150
150
(
i
i
1
i1
i1
P ( A i
) 11/
P A)
1
P(
A)
1
P(
A ) 1
P(
A ) 1
P(
A )
P(
A ).
n
n
j j
( 1
x)
C x , miviRebT, rom:
j1
n
150 2 1 2 3 1 3 4 1 4
P ( A)
C150 ( ) C150(
) C150(
) .
365 365 365 365
vinaidan, 150/365 0, 41, xolo
4
4 1 4 150 4 1 (0,41)
C150( ) ( ) 0.005 ,
365 365 24 24
amitom mwkrivis niSancvladobis gamo, Tu gadavagdebT mwkrivis
wevrebs dawyebuli me-5 wevridan (mwkrivebis zogadi Teoriidan
gamomdinare), SesaZlebelia vamtkicoT, rom
2 3
(0.41) (0.41)
PA ( ) 0.41 0.41 0.08 0.01 0.34.
2 6
magaliTi 10 (asoebis amocnoba). gvaqvs asoebis ori erToblioba:
I={К, И, З, Н} da II={З, Ч, Н}.
SemTxveviT virCevT erT erTobliobas da arCeuli erTobliobidan
erT asos. amorCeul asos Zalian mcire drois ganmavlobaSi vuCvenebT
damkvirvebels (ise rom mas ar SeuZlia mTlianad aRiqvas aso). rogoria
asos sworad gamocnobis albaToba, Tu damkvirvebelis pasuxia “Н”, roca
is asos gamosaxulebaSi dainaxavs vertikalur xazs da pasuxia “З”, roca
asos gamosaxulebaSi vertikaluri xazi ar aris?
amoxsna. SemoviRoT xdomilebebi:
A i
{ amorCeulia i urierToblioba
, i 1,2}
;
“К”, “И”, “З”, “Н” da “Ч” – iyos xdomileba, rom warmodgenilia Sesabamisad
К, И, З, Н da Ч asoebi;
B { damkvirveb elmasworad upasuxa }.
amocanis pirobebSi cxadia:
P ( A1 ) P(
A2
) 1/2;
P ( ―К‖| A
1)= P ( ―И‖| A
1)= P ( ―З‖| A
1)= P ( ―Н ‖| A
1)=1/4, P ( ―Ч‖| A
1)=0;
P ( ―З‖| A
2)= P ( ―Ч‖| A
2)= P ( ―Н‖| A
2
)=1/3, P ( ―К‖| A
2
)= P ( ―И‖| A
2
)=0.
vinaidan A 1
da A 2
qmnian xdomilebaTa srul sistemas, amitom TiToeuli
asos sworad amocnobis albaToba SegviZlia gamovTvaloT sruli
albaTobis formuliT:
P ( ―К‖)= P ( A 1
) P ( ―К‖| A
1)+ P ( A 2
) P ( ―К‖| A
2)=1/8;
P ( ―И‖)= P ( A 1
) P ( ―И‖| A
1)+ P ( A 2
) P ( ―И‖| A
2
)=1/8;
P ( ―З‖)= P ( A 1
) P ( ―З‖| A
1)+ P ( A 2
) P ( ―З‖| A
2)=7/24;
P ( ―Н‖)= P ( A 1
) P ( ―Н‖| A
1)+ P ( A 2
) P ( ―Н‖| A
2
)=7/24;
P ( ―Ч‖)= P ( A 1
) P ( ―Ч‖| A
1)+ P ( A 2
) P ( ―Ч‖| A
2
)=1/6.
n
21