The Probability Calculus.  Divide the number of positive outcomes by the total number of (equally possible) outcomes  Computations are independent of.

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Presentation transcript:

The Probability Calculus

 Divide the number of positive outcomes by the total number of (equally possible) outcomes  Computations are independent of any facts about the process that generates the outcome. As long as you know all the possible outcomes and they’re equally probable, you’re good.

 Divide the number of observed positive outcomes by the number of total observed outcomes.

 Assign a number between in the range of 0 to 1 that corresponds to your degree of belief in a proposition  The probability is a subjective degree of belief

 The Probability Calculus is a way of computing the probabilities of compound arrangements of events once each individual event has been given a probability.

 It doesn’t matter which of the described interpretations you use; the probability calculus will work regardless.

Preliminary rules: 1.The probability that an event will necessarily happen is 1. 2.The probability of an event that necessarily cannot happen is 0.

 Six additional rules

The probability of A and B occurring is equal to the probability of A times the probability of B happening given A.

 The probability calculus can be used in conjunction with the relative frequency theory and the subjectivist theory: ◦ An example of this is the mortality tables used by insurance companies. ◦ The probability calculus can also be used to evaluate odds of such events as two teams meeting in the Super Bowl.