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4.5
General Probability Rules
Previous Probability Rules
1) The probability P(
A
) of any event
A
satisfies 0
≤
P(
A
)
≤
1.
2) All possible outcomes together must have probability 1.
P(
S
) = 1.
3) Two events
A
and
B
are disjoint
→P(
A
or
B
) = P(
A
) + P(
B
)
4) The complement rule
states that→
P(
A
c
) = 1 – P(
A
)
5) Two events
A
and
B
are independent
→
P(
A
and
B
) = P(
A
)P(
B
)
General addition rules
The union
of any collection of events is the event that at least one of the collection
occurs.
The intersection
of any collection of events is the event that
all
of the events occur.
Addition rule for disjoint events
If events
A
,
B
, and
C
are disjoint in the sense that no two have any outcomes in common,
then
P (one or more of
A
,
B
,
C
) = P(
A
) + P(
B
) + P(
C
)
P (union of
A
,
B
,
C
) = P(
A
) + P(
B
) + P(
C
)
This rule extends to any number of disjoint events.
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For any two events
A
and
B
,
P(
A
or
B
) = P(
A
) + P(
B
) – P(
A
and
B
)
Example #1
Consider tossing a die once.
Let
A
be the event that you get a 1.
Let
B
be the event that
you get an odd number.
What is the P(
A
or
B
)?
Here,
A
and
B
are not disjoint.
●before (restrictive rule (4.2), holds only if
A
and
B
are disjoint):
P(
A
or
B
) = P(
A
) + P(
B
)
●now (general rule (4.5), holds whether or not
A
and
B
are disjoint):
P(
A
or
B
) = P(
A
) + P(
B
) – P(
A
and
B
)
Example #2
Consider tossing a die once.
Let
A
be the event that you get a 1.
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This note was uploaded on 02/22/2012 for the course PAM 2100 taught by Professor Abdus,s. during the Fall '08 term at Cornell University (Engineering School).
 Fall '08
 ABDUS,S.

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