Chapter 3 notes
3 AReview of Probability
General ter ms for Probability
Trial ->
single
A occur rence of
a chance experiment, such as a
single ro l l of
a die
Sample Space -> The list
o fa l l the possible outcomes of
an experiment
outcome -> possible resulto fa n experiment
Event -> Listo ffavo u r a b l e outcomes
Equally likely outcomes -> > outcomes that
h ave the same chance
occurring.
of
outcomes:
probability of
equally likely
offavo u r a b l e
P(event) number
=
outcomes
to t a l number of
o u tc o m e s
Experimental probability is calculated in the same way as theoretical probability but
uses the results of
an experiment
re s u l ts
Prevent) number
=
favo u r a b l e
of
to t a l number oft r i a l s
3B Formal Notation For Venn diagrams and two-way tables
Set -> collection of elements thatinclude numbers, letters or oth er objects
or
group
sample space -> S.r.U or 5, is the s eo
t fall possible elements or objects considered
in a
particular situation.
venn diagram > illustrates how all elements in the sample space a re distributed the
among
events
A B
Or
A #
-
A
Null -> A with
set no elements and is symbolised by 33 or
/I elements that
belong to A and m a ke
B up the Intersection AlB
, chapter 3 n o te s
3B Formal notation fo r Ven n diagrams an d t wo -way tables
·
All elements that to either eve n ts B AUB
belong A or m a ke up the Union
Two A exclusive if
Sets an d B a re mutually they have no e l e m e n ts in common,
meaning
An
=
For eve n t
A, the complement
o fA is A 1 - P(AUB) P(ani)
=
P(E) 1
=
-
P(A)
(ACB)
·
A only is defined as all the e l e m e n ts in b u tn o t
A in any other set
n(A)
·
is the number ofe l e m e n ts in A.
Set
n(A15)
venn
diagram
n(AnB)
n(AnB) - n(Fri)
A A
n(Fri) I L
/- 13 (B
B 1 - 55 -
(B)
on 13)
W
n(Ae B) B
3 1 4
3 2 51
-
n(5)
(A cny)
2
4 6 10 n(5
/ q
n(F 15)
-(A) n(F)
n(=n)
(neither n ow
A B
Mutually exclusive events and non-mutually exclusive eve n ts
for t wo eve n ts . A and B, is:
The addition rule
P(AUB) P(A) =
P(B)
+
-
P(AnB)
A B A B A B A B
AUB A B A 1 B
If A and B a re mutually exclusive then:
P(AB) 0
=
P(AUB) P(A) P(B) =
+
A B
3 AReview of Probability
General ter ms for Probability
Trial ->
single
A occur rence of
a chance experiment, such as a
single ro l l of
a die
Sample Space -> The list
o fa l l the possible outcomes of
an experiment
outcome -> possible resulto fa n experiment
Event -> Listo ffavo u r a b l e outcomes
Equally likely outcomes -> > outcomes that
h ave the same chance
occurring.
of
outcomes:
probability of
equally likely
offavo u r a b l e
P(event) number
=
outcomes
to t a l number of
o u tc o m e s
Experimental probability is calculated in the same way as theoretical probability but
uses the results of
an experiment
re s u l ts
Prevent) number
=
favo u r a b l e
of
to t a l number oft r i a l s
3B Formal Notation For Venn diagrams and two-way tables
Set -> collection of elements thatinclude numbers, letters or oth er objects
or
group
sample space -> S.r.U or 5, is the s eo
t fall possible elements or objects considered
in a
particular situation.
venn diagram > illustrates how all elements in the sample space a re distributed the
among
events
A B
Or
A #
-
A
Null -> A with
set no elements and is symbolised by 33 or
/I elements that
belong to A and m a ke
B up the Intersection AlB
, chapter 3 n o te s
3B Formal notation fo r Ven n diagrams an d t wo -way tables
·
All elements that to either eve n ts B AUB
belong A or m a ke up the Union
Two A exclusive if
Sets an d B a re mutually they have no e l e m e n ts in common,
meaning
An
=
For eve n t
A, the complement
o fA is A 1 - P(AUB) P(ani)
=
P(E) 1
=
-
P(A)
(ACB)
·
A only is defined as all the e l e m e n ts in b u tn o t
A in any other set
n(A)
·
is the number ofe l e m e n ts in A.
Set
n(A15)
venn
diagram
n(AnB)
n(AnB) - n(Fri)
A A
n(Fri) I L
/- 13 (B
B 1 - 55 -
(B)
on 13)
W
n(Ae B) B
3 1 4
3 2 51
-
n(5)
(A cny)
2
4 6 10 n(5
/ q
n(F 15)
-(A) n(F)
n(=n)
(neither n ow
A B
Mutually exclusive events and non-mutually exclusive eve n ts
for t wo eve n ts . A and B, is:
The addition rule
P(AUB) P(A) =
P(B)
+
-
P(AnB)
A B A B A B A B
AUB A B A 1 B
If A and B a re mutually exclusive then:
P(AB) 0
=
P(AUB) P(A) P(B) =
+
A B
