Summary
Tree diagrams are used to represent all possible outcomes of combined events and calculate their probabilities. They are particularly useful for events with multiple stages.
- Tree Diagram — a visual representation of all possible outcomes of an event. Example: A tree diagram showing the gender of three children.
- Combined Event — an event with two or more stages. Example: Throwing two dice at the same time.
- Independent Events — events where the outcome of one does not affect the other. Example: Drawing a pencil from a box, replacing it, and drawing again.
- Mutually Exclusive Events — events that cannot happen at the same time. Example: Rolling a die and getting either an even or an odd number.
- Conditional Probability — the probability of an event occurring given that another event has already occurred. Example: Drawing a second pencil from a box without replacing the first.
Exam Tips
Key Definitions to Remember
- Tree Diagram
- Combined Event
- Independent Events
- Mutually Exclusive Events
- Conditional Probability
Common Confusions
- Confusing independent events with mutually exclusive events
- Forgetting to multiply probabilities along the branches
Typical Exam Questions
- How do you draw a tree diagram for two dice thrown together? Draw branches for each possible outcome of the dice.
- What is the probability of both dice showing a total of eight? Calculate using the tree diagram and add the probabilities.
- How do you find the probability of drawing two red pencils without replacement? Use conditional probability and multiply along the branches.
What Examiners Usually Test
- Ability to draw and interpret tree diagrams
- Calculating probabilities of combined events
- Understanding and applying conditional probability