# Lecture06 - 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 – 47 Conditional probability The probabilities assigned to various events depend on what is known about the experimental situation when the assignment is made. What happens if we get subsequently some additional information? I.e., how does the information “an event B has occurred” affects the probability assigned to the event A ? For any two events A and B with P ( B ) > 0 , the conditional probability of A given that B has occurred is defined by P ( A | B ) = P ( A B ) P ( B ) Lindley (2006, Chapter 4), Olofsson (2007, Chapter 1 and 4)
How to calculate with probabilities (cont.) DSAP, NUS, Semester 1, 2008/2009 – 48 The Multiplication Rule: P ( A B ) = P ( B | A ) P ( A ) if P ( A ) n = 0 = P ( A | B ) P ( B ) if P ( B ) n = 0 Lindley (2006, Chapter 5), Olofsson (2007, Chapter 1)

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How to calculate with probabilities (cont.)
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Lecture06 - GEM2900 Understanding Uncertainty Statistical...

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