This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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(AB) 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,...
View Full
Document
 Fall '09
 AnthonyChan

Click to edit the document details