STAT 4105
Exam 1 – Study Sheet
=
∩
PAB
A BB
∪ = + 
A B A B A
Urn Problems
1)
Ordered Lists with Replacement
# Lists = n × n × n × … × n
k
= n
K
2)
Ordered Lists without Replacement
# Lists = n × (n1) × (n2) × … × (nk+1)
= n! / (nk)!
= (n)
k
3)
Unordered Sets without Replacement
# Sets
= (n)
k
/ k!
=
nk
Limits

/(   ) ≤
≤ 
/( )
e nk n k 1
nknk e nk n
*When limits are close together,
≈ 
/( )
nknk e nk n
Axioms of Probability
≥
PAB 0
>
PBB 0
∪
=
+

PA BC PAC PB AC
(
∩ )
PA BC PACP BA C
Discrete Probability
How to reverse a condition (Assume common condition E)
=
(
) ( )
PDC PDP CD P C
Bayes’ Theorem
=
(
) (
)=
(
) =
(
)
PBiA PBiCP ABi P AC
PBiCP ABi j 1kPBjCP ABj
Examples
There are 8 women and 11 men in a graduating class. Three are chosen to give speeches.
What is the probability that all three are women?
)=( ) (
) = .
Pall women 3 from 19
8 3 19 3 0 0578
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View Full DocumentThere are 20 pairs of similar patients.
What is the probability that a new acne cream will do better in 15 or more of the pairs?
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 Spring '08
 GRTerrell
 Statistics, Probability, Probability theory, #, Bayesian probability, PTO, 1019 PB

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