Final answer:
The student has 18 possible outcomes when randomly selecting an animal. There are 12 ways to choose a cat and 6 ways to choose a dog. The probability of choosing a dog is 1 out of 3, or approximately 33.33%.
Step-by-step explanation:
A student has a situation with 12 cats and 6 dogs at the Humane Society and is trying to determine the various probabilities involved in randomly choosing one.
A) How many possible outcomes are there?
When choosing from 12 cats and 6 dogs, there are a total of 18 possible outcomes (12 + 6 = 18).
B) In how many ways can you choose a cat?
There are 12 ways to choose a cat since there are 12 cats available.
C) In how many ways can you choose a dog?
There are 6 ways to choose a dog since there are 6 dogs available.
D) Describe the likelihood that you choose a dog. Explain reasoning.
The likelihood of choosing a dog can be represented by the probability of choosing one dog out of the total number of animals, which is 6 out of 18, or 1 out of 3 when simplified (6/18 = 1/3). This means there is a 33.33% chance of choosing a dog.