Questions: At the animal shelter where Miguel volunteers on the weekends, there were three Siamese cats, five tabby cats, eighteen mixed-breed dogs, and six iguanas in their cages. If a customer picks any of these animals at random, find the probability that the animal is either a mixed-breed dog or a Siamese cat. Express your answer as a reduced fraction.

$At the animal shelter where Miguel volunteers on the weekends, there were three Siamese cats, five tabby cats, eighteen mixed-breed dogs, and six iguanas in their cages. If a customer picks any of these animals at random, find the probability that the animal is either a mixed-breed dog or a Siamese cat. Express your answer as a reduced fraction.$

Transcript text: At the animal shelter where Miguel volunteers on the weekends, there were three Siamese cats, five tabby cats, eighteen mixed-breed dogs, and six iguanas in their cages. If a customer picks any of these animals at random, find the probability that the animal is either a mixed-breed dog or a Siamese cat. Express your answer as a reduced fraction.

Solution

Solution Steps

Step 1: Count the Total Number of Animals

To find the total number of animals at the shelter, we sum the number of each type of animal:

\[ \text{Total Animals} = \text{Siamese Cats} + \text{Tabby Cats} + \text{Mixed-Breed Dogs} + \text{Iguanas} = 3 + 5 + 18 + 6 = 32 \]

Step 2: Count the Favorable Outcomes

Next, we determine the number of favorable outcomes, which includes the mixed-breed dogs and Siamese cats:

\[ \text{Favorable Outcomes} = \text{Mixed-Breed Dogs} + \text{Siamese Cats} = 18 + 3 = 21 \]

Step 3: Calculate the Probability

The probability $ P $ that a randomly selected animal is either a mixed-breed dog or a Siamese cat is given by the ratio of favorable outcomes to the total number of animals:

\[ P = \frac{\text{Favorable Outcomes}}{\text{Total Animals}} = \frac{21}{32} \]