An animal shelter has a 58% adoption rate for puppies. Of all puppies in the shelter, 80% live to be 7 years or older. Of the puppies who are adopted, 90% live to be 7 years or older. What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years?

P (A∩B) = 0.522

Step-by-step explanation:

Let's call A the event that a puppy is adopted and B the probability that a puppy live 7 or more years

So, the probability P (A∩B) that a randomly selected puppy in the shelter will get adopted and live 7 or more years is:

P (A∩B) = P (A) * P (B/A)

Because A and B are not independents.

Then, the probability P (A) that a puppy is adopted is 58% and the probability P (B/A) that a puppy live 7 or more years given that the puppy is adopted is 90%.

Finally, replacing the values, we get:

P (A∩B) = 0.58*0.9 = 0.522

It means that the 52.2% of the puppies are adopted and live 7 or more years.