STAT 4105 - xam 1 Study Sheet

# STAT 4105 - xam 1 Study Sheet - STAT 4105 Exam 1 Study...

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STAT 4105 Exam 1 – Study Sheet = PAB |A B||B| ∪ = + - A B A B A Urn Problems 1) Ordered Lists with Replacement # Lists = n × n × n × … × n k = n K 2) Ordered Lists without Replacement # Lists = n × (n-1) × (n-2) × … × (n-k+1) = n! / (n-k)! = (n) k 3) Unordered Sets without Replacement # Sets = (n) k / k! = nk Limits - /( - - ) ≤ ≤ - /( ) e nk n k 1 nknk e nk n *When limits are close together, ≈ - /( ) nknk e nk n Axioms of Probability PAB 0 > PBB 0 = + - PA BC PAC PB AC ( ∩ ) PA BC PACP B|A C Discrete Probability How to reverse a condition (Assume common condition E) = ( ) ( ) PDC PDP C|D P C Bayes’ Theorem = ( ) ( )= ( ) = ( ) PBiA PBiCP A|Bi P A|C PBiCP A|Bi j 1kPBjCP A|Bj Examples There are 8 women and 11 men in a graduating class. Three are chosen to give speeches. What is the probability that all three are women? )=( ) ( ) = . Pall women 3 from 19 8 3 19 3 0 0578

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There are 20 pairs of similar patients. What is the probability that a new acne cream will do better in 15 or more of the pairs?
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STAT 4105 - xam 1 Study Sheet - STAT 4105 Exam 1 Study...

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