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Summary of probability rules

Summary of probability rules - Summary of probability rules...

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Summary of probability rules For an experiment with sample space S with a finite number of outcomes, and for arbitrary events A and B . Axioms: 1. 0 P ( A ) 1, 2. P ( S ) = 1, and 3. when A and B are disjoint events, P ( A B ) = P ( A ) + P ( B ). General rules: P ( A ) is the sum of the probabilities of each of the outcomes in A . Equally likely rule: If all outcomes are equally likely (have the same probability) then P ( A ) = number of outcomes in A number of outcomes in S Compliment rule: P ( A c ) = 1 - P ( A ) Union rule: For any events A and B , P ( A B ) = P ( A ) + P ( B ) - P ( A B ) Basket formula: A basket has N poker chips of which N b are blue. If we plan to randomly select a poker chip, P (“Chip is blue”) = N b /N Population formula: A population has N subjects of which N a have characteristic a . If we plan to randomly select a subject, P (“Subject has characteristic a”) = N a /N Partition rule: For any two events A and B , P ( A ) = P ( A B c ) + P ( A B ) 1

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Conditional probability rules: Definition: For events A and B with P ( B ) > 0: P ( A | B ) = P ( A B ) P ( B ) Conditional multiplication rule: P ( A B ) = P ( A | B ) P ( B ) Conditional compliment rule: For events A and B with P ( B )
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