Adog allergy test for people has a 98% accuracy rate. only 1% of the population has an allergy to dogs (actually it is much smaller than use a group of 100,000 people who've taken this test and the information provided to complete a table and answer the following question:

if you tested positive, what is the probability you have a dog allergy?

Step-by-step explanation:

For this case we cna define the following notation:

+ : represent that the test is positive

-: represent that the test is negative

A= the dog present the allergy

NA= the dog not present the allergy

We know that for this case so then by complement

The accuracy on this case is 0.98 so then we have the following probability:

Who means that if the dog present the allergy the test detect this with a 98%.

We can complet the following table with a basis of 10000 people:

                                    Test +                Test -        Total

Allergy (A)                     980                  20             1000

Not Allergy (NA)          1980                97020        99000

Total                              2960               97040        100000

And we want to find this probability:

And we can use the bayes rule for this case:

For this case we know that the probability of positive is and the probability of , so then we have: