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Chapter 15
Probability Rules
ActivStats:
15
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Chapter 15
Model of a random phenomenon
1.
The sample space S (or
Ω
)
= the set of all possible
outcomes
2.
Events
= subsets of the sample space
•
A
c
= "A does not occurs"
 the
complement
of A
•
Two events are called
disjoint
, if they cannot occur
simultaneously
•
Combined events:
A
or
B,
A
and
B
3.
Probability
= a function that to each event A assigns a
number P(A)
•
0
≤
P(A)
≤
1
•
P(S) = 1
•
P(A
c
) = 1P(A)
•
if A are B are
disjoint
, then
P(A or B) = P(A) + P(B)
Example (Model with Equally Likely Outcomes)
If the sample space has
k
possible outcomes and
all are equally likely, then
each has the probability
1/k
and the probability of an event
A is
outcomes
possioble
all
of
count
A
in
outcomes
of
count
A
P
=
)
(
Most of models do not have this property.
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View Full Document Addition Rule for disjoint events:
P(A or B) = P(A) +
P(B)
On Venn diagram the
probability
behaves as
area
.
General addition rule
P(A or B) = P(A) +
P(B)  P(A and B)
Example:
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This note was uploaded on 07/25/2008 for the course STT 200 taught by Professor Dikong during the Summer '08 term at Michigan State University.
 Summer '08
 dikong

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