Normative Theories of Probability
Probability: numerical measure of the strength of a belief in a certain proposition
Theories: frequency, logical, personal
Rule of coherence: addition, multiplication, conditional probability, independence
Frequency: Look at which chances are best to use
P(A) + p(not A) = 1
Not A is called the “complement” of A)
Mutually exclusive
Propositions A and B are “mutually exclusive” if they cannot both be true at the same
time

i.e. if one of the propositions is true, that “excludes” the possible of the other
being true: the two propositions “mutually exclude each other

When propositions A and B are mutually exclusive: p(A or B) = p(A) + p(B)

E.g. p(yes) = p(femaleyes or maleyes) = p(femaleyes) + p(maleyes)
Where does additivity come from?

From betting. The expected value of a bet on an event is its probability times the
amount to win (later we’ll see this works for expected utility)
o
For example, the expected value of “$10 if a coin comes up with heads” is
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 Fall '11
 Mellers
 Conditional Probability, Probability, Probability theory

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