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5/25/11
Lecture 11
1
STOR 155 Introductory Statistics
Lecture 11: General Probability Rules
The
UNIVERSITY
of
NORTH CAROLINA
at
CHAPEL HILL
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Lecture 11
2
Review
• Outcome, Sample space, Event
• Union (
or
), Intersection (
and
), Complement,
Disjoint, …
• Venn diagram
• Basic rules:
– For any event
A
,
P
( not
A
) = 1 
P
(
A
).
– If
A
and
B
are disjoint, then
P
(
A
B
) = 0.
– For any two events
A
and
B
,
P
(
A
B
) =
P
(
A
) +
P
(
B
) 
P
(
A
B
).
5/25/11
Lecture 11
3
General Addition Rule
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Lecture 11
4
Independence
•
A
and
B
are independent if knowing that
one occurs does not change the
probability that the other occurs.
• For independent events
A
and
B
,
P
(
A
B
) =
P
(
A
)
P
(
B
) (
Multiplication rule
)
5/25/11
Lecture 11
5
Cards (
Ex 1
)
A card is drawn from a deck of 52 playing
cards. What is the probability that the card is
 a club? (event
A
)
 a king? (event
B
)
 a club and a king? (event
A
B
)
Are
A
and
B
independent?
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Lecture 11
6
Independent vs Disjoint
•
A
and
B
are independent if and only if
P
(
A
B
) =
P
(
A
)
P
(
B
)
• If
A
and
B
are disjoint,
P
(
A
B) = 0
• Note
: If
P
(
A
) > 0 and
P
(
B
) > 0, then
disjoint
A
,
B
are
dependent
.
(
A
happens
simply implies that
B
does not happen!)
5/25/11
7
• The probability of an event measures how likely it will
occur.
• A
conditional probability
predicts how likely an event
will occur
under specified conditions
.
•
P
(
A

B
) = the conditional probability that
A
occurs
(
uncertain
), given that
B
has occurred (
certain
).
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This note was uploaded on 11/18/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Summer '08 term at UNC.
 Summer '08
 AndrewB.Nobel

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