Geometry

Question Analysis
This question involves using a tree diagram to calculate the probability of an event that can occur through two different paths (afternoon departure by bus and afternoon departure by train).
The main focus is on calculating the probability of each path and then adding them to find the total probability of the desired event.

Key Concept Explanation
The probability of an event that can happen in multiple non - overlapping ways (as represented by different paths in the tree diagram) is the sum of the probabilities of each way.
For each path, we calculate the probability by multiplying the probabilities along the branches of that path.

Step - by - Step Solution
Calculate the probability of an afternoon departure by bus:
The probability of choosing a bus is 1/4.
Given that a bus is chosen, the probability of an afternoon departure is 1/3.
So, the probability of an afternoon departure by bus is (1/4) × (1/3) = 1/12.
Calculate the probability of an afternoon departure by train:
The probability of choosing a train is 3/4.
Given th...