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1/5/10
•
Today
–
Independence
–
Multiplication and Total Probability rules
•
Friday
–
Finish Independence
–
Go over HW
•
Next week
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Conditional Probability
The following is very important:
•
Definition of Conditional Probability
•
If the event B occurs…
)
(
)
(
)

(
B
P
B
A
P
B
A
P
∩
=
1/5/10
Example
•
An organization is running a dinner
for employees with at least one son.
Given that Ms. Jones is invited to the
dinner, what is the probability that
both her children are boys?
S = { (bb) (bg) (gb) (gg)}
P(bbat least 1 boy) = P(bb and at least 1 boy)/P(at least one boy)
P(bb and 1b) = ¼
P(1b) = ¾
P(bb1b) = 1/3
So we see that the sample space we wanted has 3 outcomes, not
the 2 we mistakenly assumed at first.
Given that the one child
was a boy, we only eliminate gg from the space.
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Multiplication Rule
•
Useful in determining the
intersection of sets.
)
(
)

(
)
(
)

(
)
(
A
P
A
B
P
B
P
B
A
P
B
A
P
=
=
∩
•
An urn contains 8 red balls
and 4 white balls.
We draw
2 balls without
replacement. Assume at
each draw, each ball has
equal probability of being
chosen.
•
What is the probability that
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This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.
 Spring '08
 Rodriguez
 Statistics, Conditional Probability, Probability

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