Probability_Cheat_Sheet_2015 - Harolds Probability Cheat...

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Unformatted text preview: Harold’s Probability “Cheat Sheet” 28 December 2015 Probability Rule Notation Formula Definition ∩ = “and”, Intersection, or “∧” ∪ = “or”, Union, or “∨” ˽̅ = “not”, negation, or “¬” “And” implies multiplication. “Or” implies addition. “Not” implies negation. The occurrence of one event does not affect the probability of the other, or vice versa. The occurrence of one event affects the probability of the other event. If (|) = () Independent If ( ∩ ) ≠ 0 Dependent Disjoint/Mutually Exclusive Probability Addition Rule (“or”) Multiplication Rule (“and”) Compliment Rule / Subtraction Rule (“not”) Conditional Probability (“given that”) Total Probability Rule ( ∩ ) = 0 The events can never occur together. ( ∪ ) = () + () # () = ℎ 0 ≤ () ≤ 1 # ( ∪ ) = () + () − ( ∩ ) ( ∪ ) = () + () (if disjoint) ( ∩ ) = () (|) ( ∩ ) = () (|) ( ∩ ) = ( ∩ ) ( ∩ ) = () − ( ∩ ) ( ∩ ) = () () (if independent) ( ∪ ) = () + () = 1 () = 1 − () () = 1 − () ( ∩ ) (|) = () (|) = () (if independent) (|) = () (if independent) () = ( ∩ 1 ) + ⋯ + ( ∩ ) = (1 ) (|1 ) + ⋯ + ( ) (| ) () = ( ∩ ) + ( ∩ ̅) = () (|) + (̅) (|̅) ( ∩ ) () (|) (|) = = () () Bayes’ Theorem = () (|) () (|) + (̅) (|̅) ̅̅̅̅̅̅̅̅̅̅̅̅ ( ∪ ) ≡ ̅̅̅̅̅̅̅ () ∩ ̅̅̅̅̅̅̅ () De Morgan’s Law ̅̅̅̅̅̅̅̅̅̅̅̅ ( ∩ ) ≡ ̅̅̅̅̅̅̅ () ∪ ̅̅̅̅̅̅̅ () Copyright © 2015 by Harold Toomey, WyzAnt Tutor The compliemnt of event A (denoted ) means “not A”; it consists of all simple outcomes that are not in A. Means the probability of A given B. Is a rephrasing of the Multiplication Rule. P(A|B) is the proportion of elements in B that are ALSO in A. To find the probability of event A, partition the sample space into several disjoint events. A must occur along with one and only one of the disjoint events. Allows us to reverse the order of a conditional probability statement, and is the only generally valid method! Uses negation to convert an “or” to an “and”. Uses negation to convert an “and” to an “or”. 1 Venn Diagrams Copyright © 2015 by Harold Toomey, WyzAnt Tutor 2 ...
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