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O;f"V vFkZ'kkL=k osQ fl¼kar
uksV tksf[ke osQ fl¼kar osQ fo'ys"k.k ls iwoZ] blesa iz;ksx fd, tkus okyh oqQN èkkj.kkvksa dks le>uk ykHkdkjh
gksxkA
uksV~l vfuf'prrk ekuo thou dk ,d ekSfyd rF; gSA
laHkkO;rk (Probability)
fdlh ?kVuk dh laHkkO;rk mlosQ ?kfVr (ckjackjrk) gksus dh la[;k dk vuqikr gksrh gSA ;g ?kVukvksa dh
vuqowQy la[;k dk ?kVukvksa dh oqQy la[;k ls vuqikr gksrh gSA eku yhft, fd ,d ,slh fLFkfr gS tgk¡
laHkkfor ifj.kkeksa esa ls dksbZ ,d gks ldrk gSA mnkgj.kkFkZ] tc ,d iklk isaQdk tkrk gS rks vkus okyh la[;k
1] 2] 3] 4] 5 ;k 6 esa dksbZ Hkh ,d la[;k gks ldrh gSA
izrhdkRed :i ls]
?kVukvksa osQ ?kfVr gksus dh la[;k (Number of times event has occurred
laHkkO;rk = ——————————————————————————————
laHko ?kVukvksa dh oqQy la[;k (Total number of possible events)
D;ksafd ikls dks ?kqek, tkus ij blosQ Ng laHko ifj.kke 1] 2] 3] 4] 5 vFkok 6 gksrs gSa] buesa ls fdlh
,d ifj.kke dh lacafèkr ckjackjrk (Frequency) 1@6 = 0-167 gksrh gS tks fd izR;sd ifj.kke dh
laHkkO;rk gksrh gSA
fdlh fo'ks"k ifjfLFkfr esa] ;fn fdlh ?kVuk osQ lHkh laHko ifj.kkeksa dh lwph cukbZ tkrh gS rFkk ?kVuk dh
laHkkO;rk izR;sd ifj.kke osQ gksus ij forfjr dh tkrh gS] rks bls laHkkO;rk forj.k (Probability
Distribution) dgk tkrk gSA
mnkgj.kkFkZ] ;fn ,d flDdk mNkyk tkrk gS rFkk ^'kh"kZ* (head) vkus dh laHkkO;rk 0-6 ,oa u vkus dh
laHkkO;rk 0-4 gksrh gS] rks ;g n'kkZrk gS fd ?kVuk osQ ?kfVr gksus ;k u gksus dh laHkkO;rk dk ;ksx
1 = (0-6 + 0-4) gksrk gSA
fdlh ?kVuk osQ izR;sd ifj.kke dh lwph rFkk bldh laHkkO;rk dks rkfydk osQ :i esa n'kkZuk bldk laHkkO;rk
forj.k gS ftls uhps fn[kk;k x;k gSμ
rkfydk 1
?kVuk flDdk mNkyuk ?kVuk dh laHkkO;rk
(Event Toss of Coin) (Probability of Occurrence)
^'kh"kZ* vkus dh fLFkfr 0-6
^'kh"kZ* u vkus dh fLFkfr 0-4
1-0
laHkkO;rk forj.k dk ewY; 0 ls 1 rd vfuok;Z gSA ;fn laHkkO;rk P gS rc 0 ≤ P ≤ 1
i
i
tgk¡ i = 1] 2] -------------] n
D;k vki tkurs gSa tgk¡ dgha vfuf'prrk gS] ogk¡ tksf[ke gksrk gSA
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