Page 383 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_HINDI

bdkbZ—27% izkf;drk dk ;ksxkRed ,oa xq.kkRed fu;e

;fn nks ?kVuk,¡ ijLij viothZ gksa vkSj ,d ?kVuk osQ ?kfVr gksus dh izkf;drk P(A) rFkk nwljh ?kVuk osQ uksV
?kfVr gksus dh izkf;drk P(B) gks rks nksuksa esa ls fdlh ,d ?kVuk A ;k B osQ ?kVus dh izkf;drk P(A)
+ P(B) gksxhA bl izdkj nks ;k nks ls vfèkd ijLij viothZ ?kVukvksa esa ls fdlh ,d ?kVuk (A ;k B)
osQ ?kVus dh izkf;drk mu ?kVukvksa dh vyx&vyx O;fDrxr izkf;drkvksa dk tksM+ gSA ;g fu;e ;ksx
izes; dgykrk gSA
tSlsμ P(A ;k B) = P(A) + P(B)

;fn nks ls vfèkd ?kVuk,¡ gksa rks
P(A ;k B vkSj C...) = P(A) + P(B) + P(C) + ...
mnkgj.k (Illustration 1) : ;fn rk'k dh xM~Mh esa ls ,d iÙkk fudkyk tkrk gS rks izkf;drk Kkr dhft,
fd og ;k rks iku dk ckn'kkg gksxk ;k b±V dh csxe gksxhA

gy (Solution) : iku dk ckn'kkg ;k b±V dh osxe dk vkuk ijLij viothZ ?kVuk,¡ gSaA
1
iku osQ ckn'kkg osQ fudyus dh izkf;drk =
52
1
b±V dh csxe osQ fudyus dh izkf;drk =
52
vr% b±V dh osxe ;k iku dk ckn'kkg fudkys tkus dh izkf;drk
1 1 2 1
= + = =
52 52 52 26
;ksx izes; dk izek.k (Proof)μekuk ,d ?kVuk A m rjhdksa ls ?kfVr gks ldrh gS vkSj ?kVuk B m rjhdksa
2
1
ls rFkk ewy lEHkkO; rjhdksa dh la[;k n gSA
m m
P(A) = 1 , P(B) = 2
n n
mu rjhdksa dh la[;k ftuesa A ;k B dh ?kVuk ?kV ldh gSa = m + m 2
1
vr% A ;k B osQ ?kVus dh izkf;drkμ
m + m m m
P(A ;k B) = 1 2 = 1 + 2 = P(A) + P(B)
n n n
P(A ;k B) = P(A) + P(B)

;ksx izes; dh ifjlhek,¡μ;ksx izes; rHkh ykxw gksxh tc fuEu nks 'krs± iwjh gksaμ
(a) ?kVuk,¡ ijLij viothZ gksaA
(b) os ,d gh leqPp; ;k lewg ls lEcfUèkr gksaA

;ksx izes; dk la'kksfèkr :i&tc ?kVuk,¡ ijLij viothZ u gksaμtc nks ?kVukvksa A ,oa B esa ls ;k
rks A ;k B ;k nksuksa ?kV ldrh gksa rks ,slh ?kVuk,¡ iw.kZ :i ls viothZ ugha dgykrhaA ,sls fLFkfr esa ;ksx
izes; la'kksfèkr :i esa iz;ksx fd;k tk,xkA nksuksa ?kVukvksa osQ loZfu"B va'k dks izkf;drkvksa osQ ;ksx esa ls
?kVk fn;k tk,xkA
?kVukvksa osQ viothZ u gksus ijμ
P(A ;k B) = P(A) + P(B) – P(A vkSj B)

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