Lecture 16: Baye\'s Rule and Simpson\'s Paradox Page 4 A dog is being trained to

Question

Lecture 16: Baye's Rule and Simpson's Paradox Page 4 A dog is being trained to detect explosives by sense of smell. The dog will be given a test in which 90% of packages do not contain explosives, and 10% do. Let's assume the dog will correctly identify 94% of the packages that do contain explosives, and will correctly identify 92% of the packages that do not contain explosives. If the dog believes she has found explosives she will signal to her handler. Explosives No explosivesTotal Dog does not signal Dog does signal Total 5. What percent of the packages will the dog signal her handler? a. .006 b. 828 C. .834 d. .566 @ .166 6. Suppose the dog has just signaled. What is the conditional probability that the package actually contains explosives? a. .006 b. 828 C. .834 .566 e. .993 7. Suppose the dog has not signaled. What is the conditional probability that the package does not contain explosives? a. .006 b. .828 C. .834 d. .566 .993

Explanation / Answer

5) Percentage of packages for which the dog will signal the handler = 0.166 (option e)

6) P(contains explosives | dog does signal) = 0.094/0.166 = 0.566 (d)

7) P(no explosives | dog does not signal) = 0.828/0.834 = 0.993 (e)

Explosives No explosives Total Dog does not signal 0.1 - 0.094 = 0.006 0.92x0.9 = 0.828 0.834 Dog does signal 0.94x0.1 = 0.094 0.9 - 0.828 = 0.072 0.166 Total 0.1 0.9 1

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