Study Notes
Tree diagrams are used to show all possible outcomes of combined events and calculate their probabilities. They help represent complex situations by organizing outcomes and probabilities.
- Tree Diagram — a visual representation of all possible outcomes of an event. Example: A family with three children can have different gender combinations shown in a tree diagram.
- 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 red pencil and then a blue pencil from a box without replacement.
- Mutually Exclusive Events — events that cannot happen at the same time. Example: Rolling a die and getting either a 3 or a 4.
- Conditional Probability — the probability of an event given that another event has already occurred. Example: The probability of drawing a second red pencil after drawing the first red pencil.
Exam Tips
Key Definitions to Remember
- Tree Diagram
- Combined Event
- Independent Events
- Mutually Exclusive Events
- Conditional Probability
Common Confusions
- Forgetting to multiply probabilities along the branches.
- Confusing independent events with mutually exclusive events.
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 that two dice show a total of eight? Calculate using the tree diagram by adding probabilities of paths that sum to eight.
- How do you find the probability of drawing two red pencils without replacement? Multiply the probabilities along the branches for drawing two reds.
What Examiners Usually Test
- Ability to correctly draw and label tree diagrams.
- Calculating probabilities of combined events using tree diagrams.
- Understanding and applying the rules of multiplication and addition for probabilities.