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 written as fractions, decimals, or percentages.
- Experiment — a process that leads to one of several possible outcomes.
Example: Tossing a coin is an experiment with outcomes of heads or tails. - Event — a set of outcomes of an experiment.
Example: Getting a head when tossing a coin is an event. - Mutually Exclusive Events — events that cannot happen at the same time.
Example: Rolling a die and getting either a 3 or a 4. - Independent Events — events where the outcome of one does not affect the outcome of another.
Example: Flipping a coin and rolling a die. - 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
- Event
- Mutually Exclusive Events
- Independent Events
- Conditional Probability
Common Confusions
- Confusing mutually exclusive events with independent events
- Misunderstanding conditional probability as independent probability
Typical Exam Questions
- What is the probability of event A or B if they are mutually exclusive?
P(A or B) = P(A) + P(B) - How do you calculate the probability of two independent events both occurring?
P(A and B) = P(A) ✕ P(B) - What is the probability of event A given event B has occurred?
P(A|B) = P(A and B) / P(B)
What Examiners Usually Test
- Understanding and application of the addition law for mutually exclusive events
- Use of the multiplication law for independent events
- Calculation and interpretation of conditional probabilities