# Lecture13 - GEM2900 Understanding Uncertainty Statistical...

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DSAP, NUS, Semester 1, 2008/2009 – 1 GEM2900: Understanding Berwin Turlach Department of Statistics and Applied Probability National University of Singapore

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How to calculate with probabilities (cont.) DSAP, NUS, Semester 1, 2008/2009 – 110 The Law of Total Probability : Let A 1 , . . . , A n be mutually exclusive and exhaustive events. Then for any other event B , P ( B ) = P ( B | A 1 ) P ( A 1 ) + · · · + P ( B | A n ) P ( A n ) = n s i =1 P ( B | A i ) P ( A i ) In particular: P ( B ) = P ( B | A ) P ( A ) + P ( B | A c ) P ( A c ) Woolfson (2008, Chapter 7) Lindley (2006, Chapter 5, calls it extension of the conversation )
How to calculate with probabilities (cont.) DSAP, NUS, Semester 1, 2008/2009 – 111 Example: An urn contains 4 white and 4 red balls. Let

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Lecture13 - GEM2900 Understanding Uncertainty Statistical...

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