Probability – AQA GCSE Maths (8300)

Key Concepts

• Probability scale (0 to 1, 0% to 100%)
• Experimental vs theoretical probability
• Mutually exclusive and independent events
• Combined events: AND/OR rules
• Venn diagrams, tree diagrams, and tables
• Relative frequency and probability estimates

Definitions & Examples

• Probability: A measure of how likely an event is to happen, between 0 (impossible) and 1 (certain).
• Experimental Probability: Probability estimated from actual experiments or trials, e.g., flipping a coin 100 times.
• Theoretical Probability: Probability based on known equally likely outcomes, e.g., rolling a fair die: P(3) = 1/6.
• Mutually Exclusive: Events that cannot happen at the same time, e.g., rolling a 2 or 5 on a single die.
• Independent Events: The outcome of one event does not affect the other, e.g., flipping two coins.

Methods

• Calculate probability using P(E) = Number of favorable outcomes / Total outcomes
• Use addition rule for mutually exclusive events: P(A or B) = P(A) + P(B)
• Use multiplication rule for independent events: P(A and B) = P(A) × P(B)
• Draw and interpret Venn diagrams, tree diagrams, and tables
• Estimate probability from relative frequency of repeated experiments

Advantages & Disadvantages

• Advantages: Helps predict outcomes, supports statistical reasoning, widely applicable in science, finance, and risk assessment.
• Disadvantages: Real-life events may not be equally likely, experimental probability can be inaccurate with few trials, complex when many combined events exist.

Practice Questions

• A fair coin is flipped. Find P(Heads).
• Two dice are rolled. Find the probability of getting a 4 on both dice.
• A bag contains 3 red and 2 blue balls. Find P(red or blue).
• Use a tree diagram to find the probability of getting at least one six when rolling two dice.
• In 100 trials, an event occurred 45 times. Estimate its probability.