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Probability Theory andDistributions

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Some basic terms used in

probability1. Random Experiment(E )- Any experiment

hich results in n possible outcomes.Ex. Tossin! o" a coin# Thro in! a dice etc.$. Sample space (S)- A set o" all possibleoutcomes. Ex. %" E&Thro in! a dice thenS ' 1#$# #*#+#,

. E ent - A subset o" a sample space. E entsare denoted by capital letters.Ex. %n the abo e experiment e ent A can be!ettin! e en no. E ent / can be !ettin! a no.0 etc.

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Some basic terms used in

probability*. utually Exclusi e E ents- T o e entsare said to be m.e.e. i" simultaneous

occurance o" both is not possiblei.e.A / '2+. E3ually li4ely E ents- T o e ents aresaid to be e3ually li4ely i" the chance o"occurin! is same.i.e. in coin tossin!problem !ettin! head and tail are e.l.e.

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Some basic terms used in

probability,.Exausti e e ents- T o e ent areexausti e i" A5/ 'S.

Ex. 6ettin! e en and !ettin! odd areexausti e e ents in thro in! a diceexperiment7.%mpossible e ent- The e ent hich isnot possible to occur. The chance o"impossible e ent is 2.8. Sure e ent- The e ent hich occurs1229 "or sure e ent chance is 1.

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Some basic terms used in

probability:. ;omplementary e ent-

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Simple problems in

probabilityEx.1 A coin is tossed times >nd the probability o" !ettin!1.T o heads $. at least t o heads#

. at most 1 head *. no head.Solution& ?ere E'Tossin! a coin timesS' ???#??T#?T?#T??#TTT#TT?#T?T# ?TT1.E ent A'!ettin! $ heads

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Simple problems in

probabilityEx.$ A tic4et is dra n "rom $2 tic4ets numbered "rom1#$# #B.$2.

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Simple problems in

probabilityEx. A card is dra n "rom a pac4 o"cards hat is the probability o"!ettin!1) A heart card$)A red card

) A picture card*) A red 4in! card

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Permutation and

;ombination;ombinations are the no. o" arran!ements hereorder is not important.Permutations are the no o" arran!ements hereorder is important;ombinations are less than the permutations.Fut o" n thin! r should be ta4en in n;r and nPr

ays

here n;r ' nG= rG (n-r)G nPr ' nG=(n-r)Gr G ' r(r-1)(r-$)(r- )BBB.. .$.1,G ' ,.+.*. .$.1'7$2.

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Examples on combinationA box contains + red# * !reen and

hite balls. Three balls aredra n "rom the box. hat is theprobability that the balls are o"1) same colour .$) one o" each colour.

) t o are o" same colour.

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Theorems in probabilityAddition Theorem

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ultiplication Theorem The simultaneous occurrence o" t oe ents is sho n as

P(A /) ' P(A) P(/=A)B."ordependent e ents

P(A /) ' P(A) P(/)B."orindependent e ents

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PRF/JE -1A box contains 8 red# : blue and

1+ blac4 balls. Fne ball is dra n atA box contains 8 red# : blue and1+ blac4 balls. Fne ball is dra n atrandom "rom this box.

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PRF/JE -$ There are 122 students in a class. +2pass in athematics# *2 in Physics

and 12 in both. %" a student isselected at random# hat is theprobability that he has passed in 1) atleast one subKect $) in one subKectonly ) in both the subKects *) in noneo" the subKects +) only in Physics.

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PRF/JE -. The probability that A can sol e aproblem is *=+# that / can sol e itis $= and that ; can sol e it is =7.%" all o" them try independently

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PRF/JE -* The odds in "a our o" Asho4 !ettin!a scholarship "or "urther studies in

5.S.A. are 7&+. The odds in "a our o"Li4as !ettin! a scholarship are :&7.

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