CHAPTER 2
( S ) P ( s)
sample space : = 1
set of all possible outcomes of a random experimeut
Event subset of the
sample space ( E )
PLAM
且
P LA | B )
P (B )
时
givem
PLE ) should satisfy O ≤ PLE ) ≤ 1
P (s ) =
ifE ,
Λ E 2 =φ→ PLE ,
UE 2 } =
PLE .
3 + PCE ]
2
LA A ]
complement , A ,
' '
( E . UE 2 } ) =
E UE,
2
STEPS → UULTIPLICATION RULE
H
ways fo completug step 1 Drow tree
diagram
Hz for step 2
u 3 和fo step 3
…
…
total = n . XUzxu …
ORDER → PERMUTATION RLLE
MATTER Uniqme sequance order matters ! wlo replacement
过的元素不能再
# of permntation fora setof u items usu !
0 ! = 1
《
二
用 用
, eg componen
4 ,
how
otcatios many
combinaton ' s ?
p% = P4 :
)! = 1080
for similar objeatslr areiodenticall ※U
usharbly biggez s
thau r
U = U , + Mz + M + ur
3
…
h. icdentical 业
Uzidantical U , ! M2 ! …
hr !
…
ORDERPUESN ' → CUUBINATION RULE
T
UATTER
order odoesu't matter choose r from u
,
# P > #C
cr
刁
=
( q) =
箭! n "
-
u Cr
soumple uwforeplacewrent
→ C位 =
無 :
= 3
47 !
→ C = 4
:4 =
!
118365
iseleto
E = 3× 178365 :
53509
orwt of 50 C∵
def |samp 6 经
:
P (2 ) :
3 .
49
0
C
。一
, LECTURE 2
Addition Rule
P (σ UB ) =
PCA ) + P ( B) -
P [ AMB )
P ( AMB ) =
P (A ) + PB ) -
P [ AUB )
Couditional
Probability
)
Rule
Pro bability ofB given A
Can be writtenas
P < AMB )
PCBIA >= frP (A ) >
)
PCA
Multiplication Rule
P [ AMB ) =
P ( B 1 A] XPCA3
=
P (A | B ) × P [B )
Total
ProbabilityRule
P (B ) = PCBMA ) + PEBMA ' ]
P ( BIA ] PCBIA ) PLA ')
'
= × P ( )+ A
Indepeudence
Mutually Exclusive
if indepencleuce
A happen wornt affectB
'
P ( AMB > =
必
① P (A 1 B> =
PEA )
② P (A =
B P ( A) XP < B )
DeMorgan ' s Law
IB) = ' UB
箱B ,
'
(A A
AUB ) 与 MB
'
=
More than 1 - PL ≤ )
三
=
At least = 1 -
P ( < )
P ()
乏
most
>
At = 1 -
Less than = -
P ( ), )
入
( S ) P ( s)
sample space : = 1
set of all possible outcomes of a random experimeut
Event subset of the
sample space ( E )
PLAM
且
P LA | B )
P (B )
时
givem
PLE ) should satisfy O ≤ PLE ) ≤ 1
P (s ) =
ifE ,
Λ E 2 =φ→ PLE ,
UE 2 } =
PLE .
3 + PCE ]
2
LA A ]
complement , A ,
' '
( E . UE 2 } ) =
E UE,
2
STEPS → UULTIPLICATION RULE
H
ways fo completug step 1 Drow tree
diagram
Hz for step 2
u 3 和fo step 3
…
…
total = n . XUzxu …
ORDER → PERMUTATION RLLE
MATTER Uniqme sequance order matters ! wlo replacement
过的元素不能再
# of permntation fora setof u items usu !
0 ! = 1
《
二
用 用
, eg componen
4 ,
how
otcatios many
combinaton ' s ?
p% = P4 :
)! = 1080
for similar objeatslr areiodenticall ※U
usharbly biggez s
thau r
U = U , + Mz + M + ur
3
…
h. icdentical 业
Uzidantical U , ! M2 ! …
hr !
…
ORDERPUESN ' → CUUBINATION RULE
T
UATTER
order odoesu't matter choose r from u
,
# P > #C
cr
刁
=
( q) =
箭! n "
-
u Cr
soumple uwforeplacewrent
→ C位 =
無 :
= 3
47 !
→ C = 4
:4 =
!
118365
iseleto
E = 3× 178365 :
53509
orwt of 50 C∵
def |samp 6 经
:
P (2 ) :
3 .
49
0
C
。一
, LECTURE 2
Addition Rule
P (σ UB ) =
PCA ) + P ( B) -
P [ AMB )
P ( AMB ) =
P (A ) + PB ) -
P [ AUB )
Couditional
Probability
)
Rule
Pro bability ofB given A
Can be writtenas
P < AMB )
PCBIA >= frP (A ) >
)
PCA
Multiplication Rule
P [ AMB ) =
P ( B 1 A] XPCA3
=
P (A | B ) × P [B )
Total
ProbabilityRule
P (B ) = PCBMA ) + PEBMA ' ]
P ( BIA ] PCBIA ) PLA ')
'
= × P ( )+ A
Indepeudence
Mutually Exclusive
if indepencleuce
A happen wornt affectB
'
P ( AMB > =
必
① P (A 1 B> =
PEA )
② P (A =
B P ( A) XP < B )
DeMorgan ' s Law
IB) = ' UB
箱B ,
'
(A A
AUB ) 与 MB
'
=
More than 1 - PL ≤ )
三
=
At least = 1 -
P ( < )
P ()
乏
most
>
At = 1 -
Less than = -
P ( ), )
入
