Geometry

Question Analysis
This question uses a tree diagram to assess the understanding of calculating the probability of an event (winning a small prize) that can happen via two different routes (winning a small prize in a board game or in a card game).
The main focus is on calculating the probability of each route and then summing them up.

Key Concept Explanation
When an event can occur in multiple independent ways (as shown by different paths in the tree diagram), the probability of that event is the sum of the probabilities of each individual way.
For each path, we find the probability by multiplying the probabilities along the branches of that path.

Step - by - Step Solution
Calculate the probability of winning a small prize in a board game:
The probability of choosing a board game is 1/2.
Given that a board game is chosen, the probability of winning a small prize is 2/3.
So, the probability of winning a small prize in a board game is (1/2) × (2/3) = 1/3.
Calculate the probability of winning a small prize in a card game:
The probability of choosing a card game is 1/2.
Given th...