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# Introduction to Probability MATH 5710

Utah State University

GPA 3.66

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This 2 page Class Notes was uploaded by Benton Yundt on Wednesday October 28, 2015. The Class Notes belongs to MATH 5710 at Utah State University taught by E. Heal in Fall. Since its upload, it has received 9 views. For similar materials see /class/230411/math-5710-utah-state-university in Mathematics (M) at Utah State University.

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Date Created: 10/28/15

PROBABILITY RULES The World De nition The probability chance of event A is the proportion percentage of the time A is expected to happen when the random process is repeated over and over again Fundamental Counting Principle If event A can occur in m ways and after A occurs event B can occur in n ways then the number of ways both events A and B can occur is mX n Permutations and Combinations The number of ways k objects can be selected from n objects and arranged in order is I P quot39 n k The number of ways k objects can be selected from n objects without regard to order is quotCkkknn k Opposite Event Rule The probability that event A happens is equal to one minus the probability that A doesn39t happen PA1 PA Multiplication Rule The probability that events A and B both happen is equal to the probability that A happens times the probability that B happens given that event A has occurred PA MB PAPB A Conditional Probability Rule PA n3 PAUBF 133 if PBgt0 Addition Rule The probability that event A or event B happens is equal to the probability that A happens plus the probability that B happens minus the probability that both happen PA UB PA PB PA MB De nition Two events are independent if when one happens the probability that the other happens is unchanged Ifevents A and B are independent then PA MB PA PB l A PA PB Law of Total Probability Suppose SBIUBZUmUBn and BlnBj for iij Then for any event A PAiPABxPBI Bayes Rule Suppose SBIUBZUmUBn and BlnBj for iij And forall i PBlgt0 Then given any event A PAlBj39PBj ZPAlB39PBi i1 PBj A

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