Question

An animal shelter has a 65% adoption rate for puppies. Of all puppies in the shelter, 75% live to be 7 years or older. Of the puppies who are adopted, 80% 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

Answer 1

Answer:

52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: A puppy is adopted.

Event B: The puppy lives 7 or more years.

An animal shelter has a 65% adoption rate for puppies

This means that $P(A) = 0.65$

Of the puppies who are adopted, 80% live to be 7 years or older.

This means that $P(B|A) = 0.8$

What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(A \cap B) = P(A)*P(B|A)$

$P(A \cap B) = 0.65*0.8$

$P(A \cap B) = 0.52$

52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years