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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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