Tree Diagrams

Understanding Tree Diagrams

• A tree diagram is a visual tool used in statistics to map out possible outcomes of a series of connected events.
• Each branch of the tree denotes a possible outcome and is labelled with its associated probability.

Key Components of Tree Diagrams

• An event is illustrated as a branch. Every branch is labelled with the event it represents.
• A probability is assigned to every branch, representing the likelihood of that specific event.
• The end of the branch corresponds to an outcome.

Calculating Probability from Tree Diagrams

• The probability of a sequence of events is calculated by multiplying the probabilities along the branches of the tree that correspond to these events.
• The total probability along any complete sequence of branches (from left to right) should add up to 1.

Advantages of Tree Diagrams

• Helpful in visualising complex scenarios with many variables.
• They display all potential outcomes in an organised manner.
• Useful for calculating conditional probabilities.

Tips for Drawing Tree Diagrams

• Start the tree diagram from the left, adding branches to the right for each stage of the experiment.
• Make sure to label all branches with their corresponding event and probability.
• All root-to-leaf paths or branches must have a total probability of 1.

Tree diagrams are an essential tool in understanding and illustrating probability situations. They provide a clear, visual approach to solving complex probability problems using step-by-step processes.