Given the table below showing t<span>he
probabilities of the orphaned pets in six cities' animal shelters being
different types of animals.
</span>
City Cat Dog Dog Dog <span>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%</span><span>
Condtional probability </span><span>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 </span>orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that <span>an <span>orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%</span>
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
</span>
</span>
City Cat Dog Dog Dog <span>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%</span><span>
Condtional probability </span><span>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 </span>orphaned pet in a St. Louis animal shelter is a mastiff dog is 2.46% and the probability that <span>an <span>orphaned pet in a St. Louis animal shelter is a dog is 2.91% + 2.68% + 3.09% + 2.58% = 11.26%</span>
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