🎯 Learning Objectives
- calculate experimental probability;
- compare experimental and theoretical probability;
- understand long-run relative frequency;
- judge whether an experiment is reliable.
Introduction
This lesson develops Experimental Probability 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.
Experimental Probability
A coin lands heads 47 times in 100 tosses. Experimental P(heads)=47/100=0.47.
Why Results Differ
Random variation means a short experiment may differ noticeably from the theoretical probability. With many fair trials, relative frequency usually moves closer to the theoretical value.
Visual Comparison
Practice Questions
- A six is rolled 18 times in 120 trials. Find experimental probability.
- Compare it with theoretical probability 1/6.
- Why is 1000 trials normally more reliable than 10?
- Does experimental probability have to equal theoretical probability?
✅ Check Your Work
Show answers and working
- 18/120=3/20=0.15.
- Theoretical 1/6≈0.1667; the experimental result is slightly lower.
- More trials reduce the effect of short-run random variation.
- No. It is an observed relative frequency and may differ, especially with few trials.
🧪 Math Lab: Coin Experiment
Compare experimental and theoretical probability as the number of trials grows.
0
0
—
0.50
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.