### Video Transcript

In an animal rescue shelter, 39
percent of the current inhabitants are cats, C, and 41 percent are dogs, D. Find the probability that an
animal chosen at random is either a cat or a dog. Find the probability that an
animal chosen at random is neither a cat nor a dog.

Let’s see what we know. In an animal rescue shelter, 39
percent of the animals are cats and 41 percent of the animals are dogs. For problem one, we wanna find
the probability that an animal chosen at random is either a cat or a dog.

We know that animals can either
be a cat or a dog, but not both, which makes these mutually exclusive
events. And that means, to find the
probability of event C or D happening, we add the probability of event C and the
probability of event D. Remember, the probability of
event A occurring is the number of ways A can occur over all possible
outcomes. Probability of C would be the
probability a cat is chosen out of all possible animals.

If 39 percent of all the
animals are cats, then there is a probability of 0.39 that a cat would be chosen
out of all possible animals. In the same way, if 41 percent
of all the animals are dogs, then the probability of choosing a dog out of all
possible animals is 0.41. If we combine those two
probabilities, 0.39 plus 0.41, we see that the probability of selecting a cat or
a dog, if chosen randomly, is 0.80. That also means we know that 80
percent of the animals in the shelter are either a cat or a dog. If 80 percent of the animals
are either cats or dogs, then 20 percent of the animals are not cats or
dogs.

To find the probability that an
animal chosen at random is neither a cat nor a dog, we could find the compliment
of the probability that it is a cat or a dog. Since the compliment is
everything that is not C or D. And we find that by taking the
probability of C or D and subtracting that from one. The probability that you will
not select a cat or a dog is then 0.20.