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PROBABILITY

DEFINITION:

A probability is a measure of the likelihoo that a! e"e!ti! the future #ill happe!$ It %a! o!ly assume a "alue

bet#ee! & a! '$It %a! be %al%ulate by usi!( the follo#i!( formula:

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If the probability of a! e"e!t o%%urri!( is &) the!it is a! impossible e"e!t mea!s it #ill !e"erhappe!$

If the probability of a! e"e!t o%%urri!( is ') the!it is a %ertai! e"e!t) mea!s it #ill e*!itely

happe!$

Probability

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EXAMPLE:

si+ fa%e %ubi%al i%e is thro#! o!%e) #hat is theprobability of (etti!( a! e"e! !umber,

SOLUTION:

Number of possible out%omes- . /') 0) 1) 2) 3) .4Number of tar(ete out%omes 5e"e! !umbers6- 1 /0) 2).4

Probability

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7O8NTIN9 R8LE

5'68LTIPLI7ATION

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7ou!ti!( Rule;ultipli%atio!If a! operatio! %a! be performe i! n1  #ays) if forea%h of these a se%o! operatio! %a! be performe

i! n2 #ays) thir operatio! %a! be performe i! n3 #ays a! so o!) the! the se

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7ou!ti!( Rule; ultipli%atio!

EXAMPLE:There are three boys i! a %lass$ I! ho# ma!y#ays they %a! sit if there is !o restri%tio!s,

SOLUTION:

P- n' > n0 > n1P- 516 506 5'6

P- . #ays$

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7O8NTIN9 R8LE

506 PER8TATION

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A permutatio! is a!y arra!(eme!t of r  ob@e%tssele%te from n possible ob@e%ts$ The orer ofarra!(eme!t is importa!t i! permutatio!s$

The formula for %al%ulati!( permutatio! is:

ou!ti!( Rule; Permutatio!

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ou!ti!( Rule; Permutatio!

EXAMPLE:

0 markers are ra#! from 1 markers$ Fi! the !umberof permutatio!s that %a! be possible,

SOLUTION:

!-1r- 0The total !umber of sample poi!ts is

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7O8NTIN9 R8LE

516 7OBINATION

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A %ombi!atio! is the !umber of #ays to %hoose r  ob@e%ts from a (roup of n ob@e%ts #ithout re(ar toorer$Be%ause the orer of the sub(roup oes!t matter) the%ombi!atio! solutio!s #ill be fe#er tha! thepermutatio! solutio!s a! #ill be e+presse by the

follo#i!( formula:

ou!ti!( Rule; 7ombi!atio!

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EXAMPLE:

From 2 Republi%a!s a! 1 Demo%rats *! the !umber of

%ommittees of 1 that %a! be forme #ith 0 Republi%a!a! ' Demo%rat$

SOLUTION:

The !umber of #ays of sele%ti!( 0 Republi%a!s from 2 is

ou!ti!( Rule; 7ombi!atio!

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PROBABILITY

DITRIB8TION5'6 BINOIAL DITRIB8TION