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Conditional probabilities have very similar prop
erties to the usual “unconditional” probabili
ties.
For a ﬁxed event
B
with
P
(
B
)
>
0,
1. For every event
A
, 0
≤
P
(
A

B
)
≤
1.
2. For the sample space Ω,
P
(Ω

B
) = 1.
3. For disjoint (mutually exclusive) events
A
1
,A
2
,...,.
..
P
(
∪
n
i
=1
A
i

B
) =
n
X
i
=1
P
(
A
i

B
)
for every
n
= 1
,
2
,...,
∞
.
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View Full Document Conditional probabilities can be conditioned “even
further”
.
With 3 events,
A
,
B
and
C
,
P
(
A

B,C
) =
P
(
A
∩
B

C
)
P
(
B

C
)
.
Example
: Customers purchasing a full set of
tires at a particular store can buy either tires
made in the United States or tires made else
where.
90% of customers purchasing tires made in the
United States have tires balanced immediately
60% of customers purchasing tires made in the
United States request immediately both tire
balancing and front end alignment.
Given that a customer has purchased a full
set of tires made in the United States and re
quested tire balancing, what is the probability
that this customer has also requested a front
end alignment?
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This note was uploaded on 09/20/2010 for the course OR&IE 3500 at Cornell University (Engineering School).
 '10
 SAMORODNITSKY

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