Week 3 Wed Sept 15a - WEEK 3 Wed, Sept 15 Today: Cover...

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WEEK 3 – Wed, Sept 15 Today: Cover Sections 2-7 and 2-8 . Section 2-7. BAYES CALCULATIONS . We start with an informal approach. Example 1. (a) The prevalence of a disease is 5% in a population of 1,000 individuals. A person is selected at random from the population. What is the probability that the person has the disease? See tree diagram. Ans. 50/1,000 = 0.05 (5%) and we may write P ( D ) = 0.05. (b) A medical test to detect this disease in a person has Sensitivity 90% and Specificity 88%. A person is selected at random from the population and tested for the disease. Given that the test is positive, what is the probability that the person has the disease? See the tree diagram. Note: 90% of 50 = 45 ( Sensitivity 90%) and 88% of 950 = 846 Specificity 88%. . + 45 D 5 50 - 1,000 + 114 950 836 - Ans. 45 + 114 = 159 would test positive. Of these, 45 have the disease, 45/159 and we may write . (28.3%) Formal treatment using probability rules. Easy to execute using a tree diagram. 1
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posterior probability of B given A prior probability of B ) | ( ) ( ) | ( ) ( ) | ( ) ( ) ( ) ( ) ( ) ( ) ( ) | ( B A P B P B A P B P B A P B P A B P A B P A B P A P A B P A B P + = + = = From (2-7) From (2-14) From Multiplication Rule applied to each intersection Calculate Known ) | ( ) ( ) | ( ) ( ) | ( ) ( ) | ( B A P B P B A P B P B A P B P A B P + = (2-21) Known Known Event P(Event) 2
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A P ( A | B ) B P ( B ) A 3
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Venn Diagram. B S Exercise 2- 60 . Use tree diagram. Ans. (0.70)(0.65) + (0.30)(0.30) = 0.545 Exercise 2- 64 . Use tree diagram. Ans. (0.23)(0.75) + (0.77)(0.92) = 0.88095 Exercise 2- 66 . Use tree diagram. 4
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Ans. (0.004)(0.95)/[(0.004)(0.95) + (0.996)(0.002)] = 0.0038/0.02372 = 0.1602 Exercise 2- 68 . Students work on this in class. Only covered this in 10:20am lecture. Example 2.
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Week 3 Wed Sept 15a - WEEK 3 Wed, Sept 15 Today: Cover...

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