Understanding Probability and Tree Diagrams

This page provides a detailed exploration of probability concepts and their practical applications through tree diagrams. The content focuses on mutually exclusive events and their probability calculations, offering both theoretical understanding and practical methods.

Definition: Probability represents the ratio of successful outcomes to total possible outcomes in an event.

Highlight: For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities: P(A or B) = P(A) + P(B).

Example: In a tree diagram showing blue and red outcomes, the probabilities along different branches demonstrate how choices affect final outcomes. For instance, with 5 blue and 2 red options, the probability of selecting blue would be 5/7.

Vocabulary: Relative frequency refers to the number of times an event occurs divided by the total number of trials.

Highlight: Tree diagrams serve as visual representations where:

• Each branch represents a possible outcome
• Probabilities are shown along each branch
• The sum of probabilities at each level equals one
• Final outcomes are calculated by following paths through the tree