Lect5_L6_L7_handout2

Lect5_L6_L7_handout2 - lecture 5, Probability II...

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Unformatted text preview: lecture 5, Probability II Conditional Probability General Multiplication Rule Independence of Events Contingency Tables More Examples A Case of Stock Price “Independent” versus “Mutually Exclusive” Birthday Poker lecture 5, Probability II Outline • The Concept of Probability • Sample Spaces and Events • Some Elementary Probability Rules Conditional Probability and Independence lecture 5, Probability II Conditional Probability General Multiplication Rule Independence of Events Contingency Tables More Examples A Case of Stock Price “Independent” versus “Mutually Exclusive” Birthday Poker lecture 5, Probability II Conditional Probability Example, Conditional Probability • Professor Stein has awarded 156 A’s among 1000 students that he has taught. What’s the chance for a randomly selected student from Professor Stein’s class to obtain an A? • Can use long run relative frequency method. • Amy works 10 hours or more every week for professor Stein’s course. Amy’s really interested in knowing “What’s the chance for a student who works 10 hours or more to be awarded an A?" • Conditional Probability lecture 5, Probability II Conditional Probability General Multiplication Rule Independence of Events Contingency Tables More Examples A Case of Stock Price “Independent” versus “Mutually Exclusive” Birthday Poker lecture 5, Probability II Conditional Probability Conditional Probability • The probability of an event A, given that the event B has occurred, is called the conditional probability of A given B • Denoted as P ( A | B ) • Further, P ( A | B ) = P ( A ∩ B ) P ( B ) • Assuming P ( B ) 6 = lecture 5, Probability II Conditional Probability General Multiplication Rule Independence of Events Contingency Tables More Examples A Case of Stock Price “Independent” versus “Mutually Exclusive” Birthday Poker lecture 5, Probability II Conditional Probability Interpretation • Restrict sample space to just event B • The conditional probability P(A|B) measures the chance of event A occurring in this new sample space • In other words, if B occurred, then what is the chance of A occurring lecture 5, Probability II Conditional Probability General Multiplication Rule Independence of Events Contingency Tables More Examples A Case of Stock Price “Independent” versus “Mutually Exclusive” Birthday Poker lecture 5, Probability II Conditional Probability Interpretation, ctd • P ( A | B ) = P ( A ∩ B ) / P ( B ) • P ( B | A ) = P ( A ∩ B ) / P ( A ) lecture 5, Probability II Conditional Probability General Multiplication Rule Independence of Events Contingency Tables More Examples A Case of Stock Price “Independent” versus “Mutually Exclusive” Birthday Poker lecture 5, Probability II General Multiplication Rule General Multiplication Rule • We have P ( A | B ) = P ( A ∩ B ) / P ( B ) • Multiplying both sides by P ( B ) , we have P ( A ∩ B ) = P ( B ) P ( A | B ) • Similarly,...
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Lect5_L6_L7_handout2 - lecture 5, Probability II...

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