QMM240-W08-CondtionalProbabilityAndInd

QMM240-W08-CondtionalProbabilityAndInd - QMM240 W08...

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QMM240 W08 Conditional Probability Statistical Methods for Business I - Lecture Notes Page: 1 Conditional Probability and Independence Outline: Mutually Exclusive and Exhaustively Exclusive Event Conditional Probability and Independence I) Exclusive Events Mutually Exclusive No overlap between events Let D = event that Tigers win American League pennant Let C = event that White Sox win American League pennant D C For Mutually exclusive events the intersection equals zero, i.e., 0 ) ( C D P (note NO overlap of D and C in Venn diagram) A collection of events, E 1 , E 2 , , E k is said to be mutually exclusive if for all pairs E i E j 0 Disjoint events is another term for mutually exclusive For a collection of mutually exclusive events P ( E 1 E 2 E k ) P ( E 1 ) P ( E 2 ) P ( E k ) There are no intersections to get “double counted”
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QMM240 W08 Conditional Probability Statistical Methods for Business I - Lecture Notes Page: 2 Collectively exhaustive One of the events must occur 1 ) ( 2 1 k E E E P II) Conditional Probability and Independence Does the outcome of one event provide you information on another event? EXAMPLE - Population: Students in SBA at OU Let the Event A represent height greater than six feet Let the Event B represent gender of female Estimate P(A) = Estimate P(A) for females only Conditional Probability P ( A | B ) P ( A B ) P ( B ) A B occured has B given that A of y Probabilit ) | ( B A P And ) ( )) ( ) ( ( ) | ( ' B P B A P A P B A P since we don’t include the part of A that intersects with B Given that B has occurred, the only way that A can occur is if the outcome is in the intersection of A and B (i.e. in A B). The chance of the outcome being in A ∩B given it’s in B, is just the ratio of the A ∩B “size” to the “size” of B. P ( A | B ) P ( A B ) P ( B ) as long as P(B) > 0
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QMM240 W08 Conditional Probability Statistical Methods for Business I - Lecture Notes Page: 3
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QMM240 W08 Conditional Probability Statistical Methods for Business I - Lecture Notes Page: 4 P(A|B) is a conditional probability P(A) is called a marginal probability EXAMPLE : Fitness Center (continued from L1) Let C = {person uses fitness center} M = {person is a male} F = {female} Given P(C) = .18 P(M) = .57
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