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?

city cat dog−lhasa apso dog−mastiff dog−chihuahua dog−collie
austin 24.5% 2.76% 2.86% 3.44% 2.65%
baltimore 19.9% 3.37% 3.22% 3.31% 2.85%
charlotte 33.7% 3.25% 3.17% 2.89% 3.33%
st. louis 43.8% 2.65% 2.46% 3.67% 2.91%
salt lake city 28.9% 2.85% 2.78% 2.96% 2.46%
orlando 37.6% 3.33% 3.41% 3.45% 2.78%
total 22.9% 2.91% 2.68% 3.09% 2.58%
15.30%
18.15%
21.04%
21.84%

Given the table below showing the probabilities of the orphaned pets in six cities' animal shelters being different types of animals.


   City          Cat          Dog        Dog        Dog       Dog                                      
                         −Lhasa Apso −Mastiff −Chihuahua −Collie
Austin       24.5%      2.76%    2.86%     3.44%    2.65%
Baltimore 19.9%      3.37%    3.22%     3.31%    2.85%
Charlotte  33.7%     3.25%     3.17%     2.89%    3.33%
St. Louis  43.8%     2.65%     2.46%     3.67%    2.91%
Salt Lake
City          28.9%     2.85%     2.78%     2.96%    2.46%
Orlando   37.6%     3.33%     3.41%     3.45%    2.78%
Total        22.9%     2.91%     2.68%     3.09%    2.58%

Condtional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B).

The probability of A given B, is given by


From the table, the probability that an orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that an orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%

The probability that a randomly selected orphaned pet in a St. Louis animal shelter is a mastiff given that it is a dog, is given by