Experiment
A process producing uncertain outcomes, such as rolling a die.
🎯 Learning Objectives
- define probability and common probability terms;
- identify experiments, trials, outcomes and events;
- use the probability scale from impossible to certain;
- write probabilities as fractions, decimals and percentages.
Introduction
This lesson develops Introduction and Probability Language from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
What Is Probability?
Probability measures how likely an event is to happen. It does not predict one individual result with certainty; it describes likelihood over possible or repeated outcomes.
Every probability lies between 0 and 1 inclusive.
0
Impossible 0.5
Even chance 1
Certain
Impossible 0.5
Even chance 1
Certain
Important Language
Trial
One performance of the experiment.
Outcome
One possible result.
Event
One outcome or a collection of outcomes of interest.
Sample space
The set of all possible outcomes.
Equally likely
Every outcome has the same chance.
Practice Questions
- State the probability of an impossible event and a certain event.
- Write 0.25 as a fraction and percentage.
- For a die roll, define the event “an even number”.
- Explain why probability 1.2 is impossible.
✅ Check Your Work
Show answers and working
- Impossible=0; certain=1.
- 0.25=1/4=25%.
- The event is {2,4,6}.
- Probabilities cannot exceed 1 because 1 already represents certainty.
🧪 Math Lab: Probability Scale
Move the slider and classify the likelihood.
0.50
An even chance
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Understand the meaning of each idea before selecting a method.
- Use definitions, properties and notation consistently.
- Show working and check that the final result is sensible.