Geometry

Question Analysis
This question involves using a tree diagram to calculate the probability of a combined event.
The main focus is on identifying the two paths in the tree diagram that lead to choosing an adult pet (adult dog or adult cat) and summing up the probabilities of these paths.

Key Concept Explanation
In a tree diagram, the probability of a particular outcome is found by multiplying the probabilities along the branches of the relevant path.
When there are multiple paths to an event, we calculate the probability of each path separately and then add them together.

Step - by - Step Solution
Path 1: Choosing a dog and then an adult dog
The probability of choosing a dog is 1/3.
Given that a dog is chosen, the probability of choosing an adult dog is 1/4.
The probability of this path is (1/3)×(1/4) = 1/12.
Path 2: Choosing a cat and then an adult cat
The probability of choosing a cat is 2/3....