Study Notes
Probability is the chance or likelihood of an event happening, used in everyday decision-making.
- Probability — the chance or likelihood of an event happening. Example: The probability of obtaining heads when tossing a coin.
- Symmetry Principle — used when all outcomes are equally likely. Example: Probability of rolling a 4 on a fair die is 1/6.
- Relative Frequency — the probability of an outcome happening based on repeated trials. Example: Spinning a spinner with unequal sectors multiple times to estimate probability.
- Mutually Exclusive Events — two events that cannot occur at the same time. Example: Selecting an even number or selecting a 1 from a set of numbers.
- Independent Events — two events where the occurrence of one does not affect the other. Example: Obtaining a head on one coin and a tail on another when tossed simultaneously.
- Combined Events — events that occur at the same time or in succession. Example: Probability of drawing a red ball and a green ball from separate bags.
- Conditional Probability — the probability of an event occurring given that another event has already occurred. Example: Probability of drawing a blue marble after a red one has been drawn from a bag.
- Tree Diagrams — used to represent complex situations and calculate probabilities. Example: Multiplying probabilities across branches and adding them down branches.
Exam Tips
Key Definitions to Remember
- Probability
- Symmetry Principle
- Relative Frequency
- Mutually Exclusive Events
- Independent Events
- Combined Events
- Conditional Probability
Common Confusions
- Confusing mutually exclusive events with independent events
- Misunderstanding the use of relative frequency for estimating probability
Typical Exam Questions
- What is the probability of obtaining a 6 when rolling a fair die? 1/6
- How do you calculate the probability of two independent events occurring? Multiply the probabilities of each event.
- What is the probability of drawing two red balls from a bag without replacement? Calculate using conditional probability.
What Examiners Usually Test
- Understanding and application of probability rules
- Ability to calculate probabilities using different methods
- Interpretation of tree diagrams and their use in solving probability problems