Experimental probability (AQA GCSE Statistics): Revision Notes
Experimental probability
What is experimental probability?
Experimental probability is a way to estimate the likelihood of an event by carrying out experiments and recording the results. Unlike theoretical probability (which uses mathematical calculations), experimental probability uses real data from actual trials.
Key Formula to Remember:
Each individual experiment or test you carry out is called a trial. The more trials you perform, the more accurate your probability estimate becomes.
Understanding experimental probability through examples
Let's look at a coin-flipping experiment to see how this works in practice.
Worked Example: Coin Flipping Experiment
In this experiment, a coin was thrown 50 times, and it landed on heads 34 times.
Step 1: Apply the formula
Step 2: Interpret the result This means our estimate suggests there's a 68% chance of getting heads with this coin.
Step 3: Compare with theory Notice this is different from the theoretical probability of (50%) for a fair coin, which might suggest this coin could be biassed.
Comparing experimental and predicted results
One important use of experimental probability is to test whether something is fair or biassed. You can do this by comparing your experimental results with what you would predict if the object were fair.
Testing for Bias
For a 4-sided spinner spun 100 times:
- Expected result: Each side should come up about times
- Actual result: If side 3 came up 33 times, this is significantly more than expected
- Conclusion: The spinner might be biassed towards side 3
Worked example: analysing a 4-sided spinner
Let's work through a complete example step by step.
Worked Example: Testing a 4-Sided Spinner
Gary has a 4-sided spinner with sides labelled A, B, C, and D. He spins it 200 times and records the results:
Step 1: Calculate expected results for a fair spinner
If the spinner is fair, each side should come up the same number of times:
Step 2: Compare with experimental results
- Side A: 52 times (close to expected 50)
- Side B: 15 times (much lower than expected 50)
- Side C: 54 times (close to expected 50)
- Side D: 79 times (much higher than expected 50)
Step 3: Draw conclusions
The spinner lands on side D much more often than expected and on side B much less often than expected. This suggests the spinner is biassed in favour of side D and against side B. Sides A and C appear roughly fair.
Key principles for experimental probability
Sample size matters
The more trials you carry out, the more reliable your experimental probability becomes. This is because:
Why Larger Samples Are Better:
- Small samples can give misleading results due to chance
- Large samples smooth out random variations
- Your experimental probability gets closer to the true theoretical probability
Testing for bias
Experimental probability is particularly useful for detecting bias in real-world situations:
Steps to Test for Bias:
- Compare your results with theoretical expectations
- Look for significant differences between experimental and predicted values
- Remember that small differences might just be due to chance
Calculating experimental probability
Always use the same approach:
Essential Calculation Steps:
- Count the number of successful outcomes (the event you're interested in)
- Count the total number of trials
- Divide successful outcomes by total trials using:
- Express as a decimal or percentage
Common exam tips
Key Points to Remember:
- Show your working: Always write out the formula and substitute the numbers
- Check your arithmetic: Make sure successful outcomes don't exceed total trials
- Interpret results: Don't just calculate - explain what the probability means
- Consider sample size: Larger samples give more reliable estimates
- Look for bias: Compare experimental results with theoretical expectations
Remember!
Essential Formula and Concepts:
- Experimental probability =
- More trials lead to more accurate probability estimates
- Use experimental probability to test whether something is fair or biassed
- Always show your working clearly in exam questions
- Large differences between experimental and theoretical results may indicate bias