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Summary Probability_ShortNotes_JEE_Mains_And_Advanced
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Probability_ShortNotes_JEE_Mains_And_Advanced
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PRoGABIUTYRandom Expevfmet- t non petedctcbie oud cem es
dample spcac e- set of all possf'ble oudomes
dre
hhouwn - nis) G" ncofns toroUon nls) =2
=
Event Subset of sample spacé , wanted Oukecme&
Compiement of an evend event ood happen PMA) 1 PCA)=
-
d a a t dentn of phoh abrfly out(eme
PLA) fauoutable
Hot cas oudtomes
oPCA) SI
odds fn favt of event- awsta bie odds aganst = urfouoable Pf)
un fawutahle
PAPL) fouout oble PIA)
Suke cuend mposs'bie evert
PCA) PA) =0
sTmple event n(t)= rompound event nE]>1
\
e alusfue PlANB) =0 ,echaushile PAuG=
a y Gkely AA)= M8) , mutuolly
doesnt offect e PANG)=PA) HA)
Cpendant euen -
ocukane loonoccuance of A
Cpendant euenB occunance I non ocusrance of A ofFecB
Acd ifom theotem
Plat least one euend = PlAUB) = PA) +Pte) - P(AN8)
Plexact ly one cuend) = PLA) + P©) -20(Ane) = PlAnd) + PIho8)
Plony oneaent ) = PLA) - PlANG)
Pboth Aonde = PLAnG)
PlAUeUc) PLA) + Pe) + Plc) P(Ang) -Plenc) -PlaA) 4 P[AKnc)
= -
Plexacily 20fA8,c) AAne) + P(Bnc)+PMA) - 3P(AMeNC)
lexacily of A9c) PA)+P(e) lc) - =
20(Ane)-2e(enc)-2PlcnA)
+3Phnenc)
cndoma PHobabffy
phobabity of Aguen 8 alheady occut ed
PAIG) = e(a PAn8) PLe) #o
PCe)
MultpIfcotfon thedem
indepeciant even- PCAnB) = PCA) PLE)
PLA1B) PCAJ
A,0 h e ndepenclant - *8, A@', lg' -Adepenclant
ABe Prdependant PLANGAC) =OA) PLE) PIC)
Polu se nclepenclant- PAnS) = PCAJPLG) PL6Ac)= PCA) etc) o(an)=aa)a
Lnffnte GP
+AA A+AAAA +.. .. nfnie thlos
Tota pHobabfft4 theohem
Tiee iag nam
PUA) PCEA) PCA IE) + e(Es) P[AIES) PlEn) P(AlEn
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