19 - Normative Theories of Probability Probability...

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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(female-yes or male-yes) = p(female-yes) + p(male-yes) 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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19 - Normative Theories of Probability Probability...

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