Geometry

Question Analysis
This question involves using a tree diagram to calculate the probabilities of different vacation - destination combinations and then determining the validity of statements regarding these probabilities.
The main focus is on accurate probability calculation for each combination and understanding the property that the sum of probabilities of all possible outcomes in a probability distribution is equal to 1.

Key Concept Explanation
In a tree diagram, the probability of a particular combination of choices is calculated by multiplying the probabilities along the branches that lead to that combination.
The sum of probabilities of all possible combinations in a complete probability distribution must always equal 1.

Step - by - Step Solution
Calculate the probability of each combination:
Probability of choosing an international beach destination: (1/3)×(1/3) = 1/9.
Probability of choosing a mountain hiking spot: (1/2)×(1/4) = 1/8.
Probability of choosing a historical city: (1/6)×(1/2) = 1/12.
So A, B and C are true.
Option ...