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Notes for Chapter 4 from Stat 225
Section 4.1 Conditional Probability
Conditional Probability Let A and B be events. The probability that event B occurs
given that event A occurs is called a conditional probability, and it is denoted by:
)
(
()
PB
PA
(Α∩
Α)=
.
The event on the right side is the “given” event. It is read probability of B given A. As
long as P(A)>0, you can use the above formula. This works as long as you know the 2
probabilities on the right side. This is very useful in Venn Diagram problems. However,
for simpler cases you can also find it by the following:
(
Ν(Α ∩Β)
Ν(Α)
This second equation can be used for “simple” examples (examples where
is small
and all outcomes are known and have equal probability). Some examples where this
would work would be flipping a (fair) coin repeatedly, or rolling a (fair) dice 1 or 2 times,
etc.
N
Ω
Section 4.2 General Multiplication Rule and Law of Total Probability
General Multiplication Rule:
(
)
*
(
PA B PA PB
∩
=
Α
)
1
∩
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 Fall '08
 MARTIN
 Conditional Probability, Probability

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