Geometry

Question Analysis
This question involves using a tree diagram to calculate the probability of a compound event with multiple paths leading to the desired outcome.
The main focus is on identifying all the relevant branches in the tree diagram that result in a chocolate - flavored dessert and summing up the probabilities of those paths.

Key Concept Explanation
In a tree diagram, when there are multiple ways to achieve a particular event, we calculate the probability of each individual path and then sum them up.
Each path's probability is found by multiplying the probabilities along the branches of that path, based on the multiplication rule for probabilities.

Step - by - Step Solution
Path 1: Choosing cake and then chocolate cake
The probability of choosing cake is 2/5.
Given that cake is chosen, the probability of choosing chocolate cake is 1/2.
The probability of this path is (2/5) × (1/2) = 1/5.
Path 2: Choosing ice cream and then chocolate ice c...