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STA213lecture2.notes_1

STA213lecture2.notes_1 - Recap Venn diagrams and denitions...

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Recap Venn diagrams and definitions: union, intersection, subset, mutually exclusive Properties of set operations Definition of a probability function Example: fair coin, dart board Some theorems and inequalities Today’s outline Leftover from last time: Boole’s inequality Counting: combinations and permutations Sampling with and without replacement Enumerating outcomes and calculating probabilities Examples: birthday problem, poker hands. Boole’s Inequality If P is a probability function P ( A ) = i =1 P ( A C i ) for any partition C 1 , C 2 , . . . . P ( i =1 ) i =1 P ( A i ) for any sets A 1 , A 2 , . . . . Counting 1.2.12 How likely is it to win the lottery? 1.2.13 What is the probability of winning a knock-out tournament with 16 participants? Permutations and combinations In how many ways can 5 people form a team of 3? This is a combination . What if they also have to decide who is President, vice President and helper? This is a permutation . Methods of counting Ordered, without replacement
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