10. Animal shelters commonly use behavior evaluations to determine if a dog may have violent tendencies and as such, a risk to put up for adoption. Unfortunately, there has been little validation of these tests as it is difficult (impossible?) to determine sensitivity – if a dog tests positive for violent behavior it is not put up for adoption so it may never be known if the dog really does have violent tendencies. Patronek and Bradley (2016, J of Veterinary Behavior, 15:66-77) consider a range of plausible scenarios. One scenario has the specificity (P[test is negative | dog is non-violent]) of 36% and a sensitivity (P[test is positive | dog is violent]) of 92%. If the prevalence of violent dogs is 14%, what is the probability that a randomly selected dog who tests positive is violent?
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