slide1-probability

slide1-probability - Introduction to Probability Professor...

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Introduction to Probability Professor Erkut Ozbay Economics 300
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1 ) Which of the following is more likely to be a Powerball winner? A) 32 11 5 24 18 3 B) 1 2 3 4 5 6 2) Here are the results of 9 coin flips: HHHHHHHHH What is the most likely outcome for the 10 th coin? 3) Why is a royal flush in spades the highest hand in poker? (10, Jack, Queen, King and Ace, all in spades)
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Definition of Probability The probability that an event A will occur is written as P(A) and is read “the probability of A”. Three Different Types of Probability : 1. Theoretical 2. Empirical 3. Subjective
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Vocabulary of Probability Theory Experiment - anything that produces an outcome Examples: flipping a coin, rolling a die Outcome - a particular result of an experiment Examples: coin lands heads, die roll is 5 Sample space - set of all possible outcomes of an experiment Examples: S = {Heads, Tails} S= {1,2,3,4,5,6} Event - an outcome or a set of outcomes that are of interest to the experimenter
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Probability Rules for Equally Likely Events In S where outcomes are equally likely, then the probability of event A, P(A) is P(A) = Number of ways that A can occur Total # of possible outcomes Approach is called Classical Theoretical Probability = N n A
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A Simple Experiment Suppose we were to roll a die: What is the sample space? S = {1, 2, 3, 4, 5, 6} Event 3 = die lands on 3, P(3) = 1/6 Event Even = die lands on even number, P(Even) = 3/6 = 1/2
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Another Simple Experiment Selecting a card from a deck of cards Event Q = the Queen of Hearts is selected, P( Q ) = 1/52 Event Q = a Queen is selected, P(Q) = 4/52 = 1/13 Event = a Heart is selected, P( ) = 13/52 Event KQJ = a face card is selected, P(KQJ) = 12/52 = 3/13
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Rules about Probabilities 0 ≤ P(A) ≤ 1, the probability of an event must be a number between 0 and 1, inclusive P(S) = 1, the probability of the entire sample space must be equal to 1 If an event must happen, P(A) = 1 If an event is impossible, P(A) = 0
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This note was uploaded on 12/04/2011 for the course ECON 300 taught by Professor Cramton during the Fall '08 term at Maryland.

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slide1-probability - Introduction to Probability Professor...

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