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5.1 Introducing Probability
Def’n: An experiment
is a process that, when performed, results in one and only one of
many observations.
These observations are called the outcomes
of the experiment.
Probability
is a numerical measure of likelihood that a specific outcome occurs.
3 Conceptual Approaches to Probability
:
1) Classical probability
 equally likely outcomes
exist when two or more outcomes have the same probability
of occurrence

classical probability rule
:
P
(
A
) = (# of outcomes favourable to
A
) / (total # of outcomes for experiment)
2) Relative frequency concept of probability
 experiment repeated
n
times to simulate probability
 relative frequencies are NOT probabilities, they only approximate them.

Law of Large Numbers
: If an experiment is repeated again and again, the prob. of an
event obtained from the relative frequency approaches the actual or theoretical prob.
3) Subjective probability
 subjective probability
is the degree of belief that an outcome will occur, based on the
available information
5.2/5.3 Calculating Probability
Def’n: A sample space
(a.k.a.
S
) is the set of all outcomes of an experiment.
An event
(a.k.a.
A
) is a subset of elementary outcomes;
.
S
A
⊂
Æ
P
(
A
) = probability that
A
occurs
•
A
union
of 2 events is denoted by
A
or
B
(or
B
A
U
).
•
An
intersection
of 2 events is denoted by
A
and
B
(or
B
A
I
).
•
A
complement
of an event is denoted by
A
C
.
A Venn diagram
is a picture that depicts S (events above drawn in class).
Experiment
Outcomes
Sample Space
Toss a coin
Head, Tail
S = { H, T }
Toss 2headed coin Head
S = { H }
Toss a $5 bill
Get it back, Lose money
S = { Lucky, Not Smart }
Pick a suit
Spades, Clubs, Diamonds, Hearts
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 Winter '07
 HenrykKolacz
 Probability

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