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class02 - Probability Statistics for Business Control and...

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Statistics for Business Control and Regression Analysis – Spring 2008 1 Probability Probability
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Statistics for Business Control and Regression Analysis – Spring 2008 2 Probability Probability Probability is the basic language of statistics Probability vs Statistics Probability: “a fair coin is tossed 10 time; what is the probability of getting 8 heads?” Statistics: “a coin is tossed 10 times, showing 8 heads; is the coin fair?” Origins of probability: card/dice games, gambling
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Statistics for Business Control and Regression Analysis – Spring 2008 3 Experiments, Outcomes, and Sample Spaces Experiments, Outcomes, and Sample Spaces An experiment governed by chance has several possible outcomes The collection of all possible outcomes in an experiment is the sample space , denoted by S Examples Tossing a coin Rolling a die Rolling two dice
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Statistics for Business Control and Regression Analysis – Spring 2008 4 Probability Events Probability Events Event = a collection of possible outcomes in an experiment A die rolls 5 or higher It will rain tomorrow Usually denoted by capital letters = the event “not A” ( complementary event) If A = “a die rolls 5 or higher”, = “a die rolls 4 or lower” If A = “profit in 6 consecutive quarters”, = ? P(A) = Probability of event A A A A
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Statistics for Business Control and Regression Analysis – Spring 2008 5 Properties of Probability Properties of Probability 0 P(A) 1 always sometimes use a 0–100 percent scale P(A) = 0 means that A is impossible P(S) = 1 P(A) + P( ) = 1 A
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Statistics for Business Control and Regression Analysis – Spring 2008 6 Interpretations of Probability Interpretations of Probability In an experiment with N equally likely outcomes: P(A) = (no. of outcomes in the event A)/N Long-run relative frequency: when an experiment is repeated n times (n is large), P(A) (no. of times A occurred)/n Subjective probability P(A) = degree of confidence in A
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