A veterinarian has invented an allergy test for cats. Sam the cat seems to be allergic to tina the dog. If 2% of cats are allergic to dogs and the vet's allergy test correctly indicates an allergy 98% of the time and only gives a false positive result 0.5% of the time, what is the probability sam is allergic to tina given the allergy test comes back positive?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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A veterinarian has invented an allergy test for cats. Sam the cat seems to be allergic to tina the dog. If 2% of cats are allergic to dogs and the vet's allergy test correctly indicates an allergy 98% of the time and only gives a false positive result 0.5% of the time, what is the probability sam is allergic to tina given the allergy test comes back positive?

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