Econ171-Spring2010-03-Prob2-handout

Econ171-Spring2010-03-Prob2-handout - Economics 171 171...

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Economics 171 Decisions Under Uncertainty . Preliminary Concepts in 2. Preliminary Concepts in Probability Theory pring 2010 Spring 2010 Herb Newhouse 1 eadings Readings achina eader Machina Reader – Handout 2: p. 13 – 14. • A probability or statistics book for material on Bayes’ Law. • Lindley – Ch. 6: 6.1, 6.3 – 6.4, 6.6 – 6.15 2 utline Outline onditional probability and Bayes’ Law Conditional probability and Bayes Law. • Compound lotteries and probability ixtures mixtures. 3 onditional Probability Conditional Probability Let be the set of possible states for a problem. We call the sample space. Sa l l S Let and each be a set of possible states. 0 th th diti l b bilit AB B    If 0, then the conditional probability of given , denoted | is PB P A B | PAB   PA B 4
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What can happen if we draw two integers from 1 to 4?     12,13,14,21,23,24,31,32,34,41,42,43 Let be all combinations where the second draw is even. 12 states S A     12,14,24,32, 6 sta 34,42 Let be al tes l combin A B ations where the first draw is even.   21,23,24,41,42,43 6 states B The first draw is even. What's the probability of getting even on the second draw?   2 1 12 | 6 3 PA B PAB P B  12 5 Bayes’ Law     Conditional probability: | P AB P B We can rewrite this as: | Simlarly: PA B PABPB  | PA B PBAPA Bayes' Law: | PA AB PBA       || PAB PBA PB 6 pplication of Bayes’ Law Application of Bayes Law Assume there is an equal chance that a drug is successful 60% or 80% of the time.
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Econ171-Spring2010-03-Prob2-handout - Economics 171 171...

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