1.2. DISCRETE PROBABILITY DISTRIBUTIONS
21
we see that
2
m
(C) + 2
m
(C) +
m
(C) = 1
,
which implies that 5
m
(C) = 1. Hence,
m
(A) =
2
5
,
m
(B) =
2
5
,
m
(C) =
1
5
.
Let
E
be the event that either A or C wins. Then
E
=
{
A,C
}
, and
P
(
E
) =
m
(A) +
m
(C) =
2
5
+
1
5
=
3
5
.
±
In many cases, events can be described in terms of other events through the use
of the standard constructions of set theory. We will brieFy review the de±nitions of
these constructions. The reader is referred to ²igure 1.7 for Venn diagrams which
illustrate these constructions.
Let
A
and
B
be two sets. Then the union of
A
and
B
is the set
A
∪
B
=
{
x

x
∈
A
or
x
∈
B
}
.
The intersection of
A
and
B
is the set
A
∩
B
=
{
x

x
∈
A
and
x
∈
B
}
.
The di³erence of
A
and
B
is the set
A

B
=
{
x

x
∈
A
and
x
±∈
B
}
.
The set
A
is a subset of
B
, written
A
⊂
B
, if every element of
A
is also an element
of
B
. ²inally, the complement of
A
is the set
˜
A
=
{
x

x
∈
Ω and
x
±∈
A
}
.
The reason that these constructions are important is that it is typically the
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 Spring '09
 scf
 Set Theory, Discrete Probability Distributions

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