Page 384 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

vFkZ'kkL=k esa lkaf[;dh; fof/;k¡

uksV

fp=k % 27-1

leqPp; :i esaμ
P(A ∩ B) = P(A) + P(B) – P(A ∩ B)
rhu ?kVukvksa osQ fy, ;ksx&izes; dk la'kksf/r :iμ
P(A ;k B ;k C)
= P(A) + P(B) + P(C) – P(AB) – P(AC) – P(BC) + P(ABC)
la;ksxkuqikr (Odds)μtc dHkh izkf;drk dks fdlh ?kVuk osQ i{k vFkok foi{k osQ :i esa O;Dr fd;k

tkrk gS rks bls izkf;drk la;ksxkuqikr dgrs gSaA i{k osQ la;ksxkuqikr dk igyk vad P vkSj nwljk q osQ vuq:i
gksrk gS rFkk foi{k osQ la;ksxkuqikr esa igyk vad q vkSj nwljk P osQ vuq:i gksrk gSA bu vuqikrksa dks izkf;drk
osQ eki esa fuEu fu;eksa osQ vuqlkj cnyk tkrk gSμ
P
(a) i{k dk la;ksxkuqikr (P : q) – ?kVus dh izkf;drk =
P + q
q
(b) foi{k dk la;ksxkuqikr (q : P) – u ?kVus dh izkf;drk =
P + q

mnkgj.k (Illustration 2) : nks iklksa osQ ,d ckj isaQdus ij 2 ;k 8 ;k 12 dk ;ksx izkIr gksus dh izkf;drk
Kkr dhft,A
gy Solution : nks ikls isaQdus ij oqQy ifj.kkeksa dh la[;k = 6 × 6 = 36
1
2 dk ;ksx (1, 1) izkIr gksus dh lEHkkouk =
36
5
8 dk ;ksx (6, 2), (5, 3), (4, 4), (3, 5), (2, 6) dh lEHkkouk =
36
1
12 dk ;ksx (6, 6) izkIr gksus dh lEHkkouk =
36
1 5 1 7
vr% 2 ;k 8 ;k 12 dk ;ksx izkIr gksus dh izkf;drk = + + + =
36 36 36 36
mnkgj.k (Illustration 3) :

,d O;fDr 6 esa ls 5 fu'kkus lgh yxkrk gS tcfd nwljk 5 esa ls 4 fu'kkus lgh yxkrk gSA ;fn nksuksa gh
O;fDr iz;kl djsa rks lgh fu'kkuk yxkus dh izkf;drk Kkr dhft,A
5
gy (Solution) : igys O;fDr (A) osQ lgh fu'kkuk yxkus dh izkf;drk gS vkSj nwljs O;fDr (B) osQ
6
y{; Hksnu dh izkf;drk = 4/5.
;s nksukas ?kVuk,¡ ijLij viothZ ugha gS D;ksafd A o B nksuksa y{; Hksn dj ldrs gSaA vr% lw=kkulkj]
P(A or B) = P(A) + P(B) – P(A and B)

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