, Probability (likelihood of an event happening
Terminology range : 0 - 1
outcome + experiment
·
result of decimal
·
event -
h
collection
denotated
of
as
outcomes
E (number
that
of
satisfy
outcomes
a certain
n(E)
condition
! percentage
simplified Fraction
dependant events - ist effects other outcomes
·
event the
·
independant events -
events do not affect each other's outcome PLAandBl = P(A) XP(B)
·
cards in a deck -
>
52
suits in deck 4
·
-
a
·
specific card + 4
sample spaces experiment
·
- all possible outcomes of the
unbiased
·
all
-
events are equally likely to happen
mutually exclusive whose probabilities
·
evente those events
complimentary 2 sum of to 1
=
.
Theoretical Probability :
(E) number possible sample set
·
P =
of times event can occur s =
number of possible outcomes A event A
·
=
=
B event B
·
=
n(E) ·
AUB :
A union (or) B
n(S) ·
An B =
A intersection (and) B
Experimental Probability : Addition Rule (OR/ + ) :
↑ (E) =
number of times the event occurred P(A or B) =
PLA) +
PLB)
-
PLA and Bl
number of trials done or
↑ (A and B) =
P(A) + p(B) -
P(Aor By
using venn
Diagrams :
x
S
Al
=
E
↳ sample
space *
events
event A A and B are
complimentary
if exclusive and
they are
mutually
exhaustive
left overs not involved .
compliment of an P(A))
=
1 -
PLA)
event
S S
A B exhaustive : A B
mutually exclusive :
12 12
56 covers all elements 56 no elements in common
34 34
in sample set (no overlap
9 *
occur at the time
same
PCA and B) = ·
PLAor B) =
PLA) + PLB)-PLA and B)
or
PLAUB) P(A) P(B) PLANB)
·
=
+ -
Inclusive Events : Pla and B) O
if true then
↑ (A anc B) = 0
, events
inspecting events union of
W
↑
A and B A or B
PLAorB) + PLANB) PLAorB) - PLAUB)
* note be and B's
in
diagrams intersection amount must event rotal .
: A
venn - -
from
Tree Diagrams :
branches
multiply along
& and
S
M
outcome
-
outcome outcome 2 Or
n
outcome 3 add up the results
choices you need
outcome
V outcome 2 outcome 2 sor
outcome 3 -
~
V
1st event 2nd event total =
S
of events
sequence
1
independent Events :
2
Dependent Events :
↑ and B do not influence each other ↑ and B do influence each other's results
↳ h
eg . weather , they ger replaced .
eg items not replaced
r
P (A and B) = P(A) X P(B) &
PLA and Bl =
P(A) X PLBIA)
LHS =
RIS must !
6 otherwise disproves + work separate sides !
* !
Note : 1st multiply across then add
contingency tables :
&
A table in which
frequencies correspond to a variables
I variable used to
categorize rows and the other used to
categorize columns .
Colour Blue Green Brown Total
Eye
4 5 7 16
Male
S 2 5 15
Female
Total 12 7 12 3
Terminology range : 0 - 1
outcome + experiment
·
result of decimal
·
event -
h
collection
denotated
of
as
outcomes
E (number
that
of
satisfy
outcomes
a certain
n(E)
condition
! percentage
simplified Fraction
dependant events - ist effects other outcomes
·
event the
·
independant events -
events do not affect each other's outcome PLAandBl = P(A) XP(B)
·
cards in a deck -
>
52
suits in deck 4
·
-
a
·
specific card + 4
sample spaces experiment
·
- all possible outcomes of the
unbiased
·
all
-
events are equally likely to happen
mutually exclusive whose probabilities
·
evente those events
complimentary 2 sum of to 1
=
.
Theoretical Probability :
(E) number possible sample set
·
P =
of times event can occur s =
number of possible outcomes A event A
·
=
=
B event B
·
=
n(E) ·
AUB :
A union (or) B
n(S) ·
An B =
A intersection (and) B
Experimental Probability : Addition Rule (OR/ + ) :
↑ (E) =
number of times the event occurred P(A or B) =
PLA) +
PLB)
-
PLA and Bl
number of trials done or
↑ (A and B) =
P(A) + p(B) -
P(Aor By
using venn
Diagrams :
x
S
Al
=
E
↳ sample
space *
events
event A A and B are
complimentary
if exclusive and
they are
mutually
exhaustive
left overs not involved .
compliment of an P(A))
=
1 -
PLA)
event
S S
A B exhaustive : A B
mutually exclusive :
12 12
56 covers all elements 56 no elements in common
34 34
in sample set (no overlap
9 *
occur at the time
same
PCA and B) = ·
PLAor B) =
PLA) + PLB)-PLA and B)
or
PLAUB) P(A) P(B) PLANB)
·
=
+ -
Inclusive Events : Pla and B) O
if true then
↑ (A anc B) = 0
, events
inspecting events union of
W
↑
A and B A or B
PLAorB) + PLANB) PLAorB) - PLAUB)
* note be and B's
in
diagrams intersection amount must event rotal .
: A
venn - -
from
Tree Diagrams :
branches
multiply along
& and
S
M
outcome
-
outcome outcome 2 Or
n
outcome 3 add up the results
choices you need
outcome
V outcome 2 outcome 2 sor
outcome 3 -
~
V
1st event 2nd event total =
S
of events
sequence
1
independent Events :
2
Dependent Events :
↑ and B do not influence each other ↑ and B do influence each other's results
↳ h
eg . weather , they ger replaced .
eg items not replaced
r
P (A and B) = P(A) X P(B) &
PLA and Bl =
P(A) X PLBIA)
LHS =
RIS must !
6 otherwise disproves + work separate sides !
* !
Note : 1st multiply across then add
contingency tables :
&
A table in which
frequencies correspond to a variables
I variable used to
categorize rows and the other used to
categorize columns .
Colour Blue Green Brown Total
Eye
4 5 7 16
Male
S 2 5 15
Female
Total 12 7 12 3
