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9/23/11
Welcome to the Jungle!
http://
www.ebaumsworld.com/audio/play/820440/
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Outline
•
Definitions of
probability
•
Structure of probability
•
Unions
•
Intersections
•
Independent events
•
Dependent events
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•
Classical
•
Empirical or Relative
Frequency
•
Mixture (Bayesian)
Definitions of Probability
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•
You flip a coin 10 times, and 7
times the coin lands on
heads.
What is the
probability that you will have
a heads on the next flip?
Example
9/23/11
•
You flip a coin 10 times, and 7 times
the coin lands on heads.
What is the
probability that you will have a heads
on the next single flip of the coin?
Classical
successes
possible
of
number
outcomes
possible
of
number
total
:
)
(
n
e
=
=
=
N
Where
N
E
P
n
e
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•
Number of outcomes leading to the
event
divided by the total number of
outcomes possible
•
Each outcome is equally likely
•
Determined a
priori

before
performing the experiment
Classical Probability
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Culture
•
From
Calculus, Volume II
by Tom M.
Apostol (2nd edition, John Wiley &
Sons, 1969 ):
•
"A gambler's dispute in 1654 led to
the creation of a mathematical
theory of probability by two famous
French mathematicians, Blaise Pascal
and Pierre de Fermat. Antoine
Gombaud, Chevalier de Méré, a
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•
You flip a coin 10 times, and 7 times
the coin lands on heads.
What is the
probability that you will have a heads
on the next flip?
•
Frequency of interest:
7
•
Total frequency:
10
•
P(H) = 7 / 10 = .7
Empirical or Relative
Frequency Probability
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Relative Frequency Probability
•
Relative Frequency of Occurrence
method – the probability of an
event is equal to the number of
times the event has occurred in
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This note was uploaded on 09/23/2011 for the course QMST 2333 taught by Professor Mendez during the Fall '08 term at Texas State.
 Fall '08
 Mendez

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