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Math 151 – Probability
Spring 2011
Jo Hardin
Probability Rules Handout
Probability Deﬁnitions
•
The
probability
of an outcome refers to how often the outcome would occur in the
long run if a random process were repeated over and over under identical conditions
(relative frequency interpretation).
•
An
experiment
is any activity or situation in which there is uncertainty about the
outcome.
•
The
sample space
is the list of all possible outcomes of a random trial. (Called
S
.)
•
An
event
is any potential subset of the sample space.
•
A
simple event
is an event consisting of exactly one outcome.
•
Two events are
mutually exclusive
or
disjoint
if they cannot both occur simultane
ously.
•
Two events are
independent
if the occurrence of one does not change the probability
that the second will occur.
Set Theory
Consider three events.
A
:
{
woman has a tattoo
}
B
:
{
someone age 1829 has a tattoo
}
C
:
{
someone has a tattoo
}
A
⊂
C B
⊂
C
because both A and B are subsets of C
Empty Set
Is the set with no outcomes and is denoted:
∅
.
Union
The union of A and B is deﬁned to be the event containing all outcomes that belong
to A alone, to B alone, or to both A and B:
A
∪
B
.
A
∪
B
=
B
∪
A
A
∪
A
=
A
A
∪ ∅
=
A
A
∪
S
=
S
if
A
⊂
B
⇒
A
∪
B
=
B
A
∪
B
∪
C
= (
A
∪
B
)
∪
C
=
A
∪
(
B
∪
C
) (associative)
If we have
n
separate events,
A
1
,A
2
,...,A
n
,
A
1
∪
A
2
∪ ··· ∪
A
n
=
∪
n
i
=1
A
i
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View Full DocumentIntersection
The intersection of A and B is deﬁned as the events in
both
A and B:
A
∩
B
=
AB
.
A
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 Spring '10
 JO.H
 Probability

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