Geometry

Question Analysis
This question uses a tree diagram to test the concept of probability addition.
The main focus is on identifying the two separate paths in the tree diagram that lead to the desired outcomes (choosing a croissant or an omelette), calculating the probability of each path, and then adding these probabilities together.

Key Concept Explanation
When dealing with mutually - exclusive events (events that cannot happen at the same time) represented in a tree diagram, the probability of either event occurring is the sum of their individual probabilities.
To find the individual probabilities, we multiply the probabilities along the branches of each relevant path in the tree diagram.

Step - by - Step Solution
Calculate the probability of choosing a croissant:
The probability of choosing a pastry is 1/3.
Given that a pastry is chosen, the probability of choosing a croissant is 1/2.
So, the probability of choosing a croissant is (1/3) × (1/2) = 1/6.
Calculate the probability of choosing an omelette:
The probability of choosing an egg dish is 2/3.