Geometry

Question Analysis
This question involves using a tree diagram to calculate the probability of a specific number of occurrences of an event (getting heads) in multiple trials (coin flips).
The main focus is on identifying all the paths in the tree diagram that result in exactly two heads and summing up the probabilities of those paths.

Key Concept Explanation
In a tree diagram for independent events like coin flips, the probability of each path is found by multiplying the probabilities along the branches of that path.
To find the probability of a particular outcome (such as getting exactly two heads), we need to find all the paths that match this outcome and add their probabilities together.

Step - by - Step Solution
Identify the paths that result in exactly two heads:
Path 1: Head, Head, Tail. The probability of this path is (1/2) × (1/2) × (1/2) = 1/8.
Path 2: Head, Tail, Head. The probability of this path...