Question

The probabilities of the orphan pets in the animal shelters of six cities being different types of animals are given in the table.CityCatDogLhasa ApsoDogMastiffDogChihuahuaDogCollieAustin24.5%2.76%2.86%3.44%2.65%Baltimore19.9%3.37%3.22%3.31%2.85%Charlotte33.7%3.25%3.17%2.89%3.33%St. Louis43.8%2.65%2.46%3.67%2.91%Salt LakeCity28.9%2.85%2.78%2.96%2.46%Orlando37.6%3.33%3.41%3.45%2.78%Total22.9%2.91%2.68%3.09%2.58%If a randomly selected orphan pet in an animal shelter of Charlotte is a dog, what is the probability that it is a Chihuahua?

Answer 1

For the city of Charlotte, these are the probabilities:

Cat: 33.7%

Dog Lhasa Apso: 3.25%

Dog Mastiff: 3.17%

Dog Chihuahua: 2.89%

Dog Collie: 3.33%

Since the selected pet is a dog, the only possibilities are it is a Lhasa Apso, a Mastiff, a Chihuahua, or a Collie.

Therefore, applying the Bayes theorem, we know that the probability that it is a Chihuahua is:

P(Chihuahua|Dog) = [P(Dog|Chihuahua)*P(Chihuahua)]/P(Dog)

P(Dog|Chihuahua) = 100% = 1

P(Chihuahua) = 2.89% = 0.0289

P(Dog) = 3.25% + 3.17% + 2.89% + 3.33% = 12.64% = 0.1264

P(Chihuahua|Dog) = 0.0289/0.1264 = 0.2286 = 22.86%