Question

The probabilities of the orphaned pets in six cities' animal shelters being different types of animals are given in the table. If a randomly selected orphaned pet in a St. Louis animal shelter is a dog, what is the probability that it is a mastiff?

Answer 1

Answer Choices:
15.30%

18.15%

21.04%

21.84%

Answer 2

Do you have the table?

Answer 3

@kirbykirby

Answer 4

What you need to do is look at the St-Louis category only. Now, since they are picking from the dogs only, then you only consider the dogs.

For all the dogs: you have 2.65+2.46+3.67+2.91 = 11.69
Now, the probability of getting a Mastiff is 2.46/11.69 = 0.2014 = 21.04%

Why can we do this? Because these percentages are just proportions. We don't have the raw numbers of dogs given, but that's ok. If this troubles you, you can think of multiplying all these numbers by 100, so you have 246 Mastiffs and 1169 dogs. Thus, the probability of getting a mastiff is 246/1169 = 0.2104

This is really just a form of a conditional probability:\[
P(\text{Mastiff}\mid\text{a dog})=\frac{P(\text{Mastiff} \cap \text{a dog})}{P(\text{a dog})}\]

Answer 5

thank you @kirbykirby I understand now

Answer 6

:) yw

Answer 7

21.04% is the answer