Summary
Probability is the maths of chance, expressed as a number between 0 and 1, indicating how likely an event is to occur. Probabilities can be expressed as fractions, decimals, or percentages.
- Experiment — a process that leads to one of several possible outcomes. Example: Tossing a coin is an experiment with two possible outcomes: heads or tails.
- Event — a set of outcomes of an experiment. Example: Getting a head when tossing a coin is an event with one favourable outcome: head.
- Mutually Exclusive Events — events that cannot happen at the same time. Example: Rolling a die and getting either a 3 or a 4 are mutually exclusive events.
- Independent Events — events where the occurrence of one does not affect the other. Example: Flipping a coin and rolling a die are independent events.
- Conditional Probability — the probability of an event occurring given that another event has already occurred. Example: The probability of drawing an ace from a deck of cards given that a king has already been drawn.
Exam Tips
Key Definitions to Remember
- Experiment: A process that leads to one of several possible outcomes.
- Event: A set of outcomes of an experiment.
- Mutually Exclusive Events: Events that cannot happen at the same time.
- Independent Events: Events where the occurrence of one does not affect the other.
- Conditional Probability: The probability of an event occurring given that another event has already occurred.
Common Confusions
- Confusing mutually exclusive events with independent events.
- Misunderstanding conditional probability as being the same as regular probability.
Typical Exam Questions
- What is the probability of drawing a red card from a deck of cards? Answer: 1/2
- If two dice are rolled, what is the probability of getting a sum of 8? Answer: 5/36
- What is the probability of drawing an ace given that a king has already been drawn? Answer: 4/51
What Examiners Usually Test
- Ability to calculate probabilities using addition and multiplication laws.
- Understanding of mutually exclusive and independent events.
- Application of conditional probability in various scenarios.