GCSE Maths Practice: theoretical-vs-experimental-probability

Experimental Probability Using Dice

Experimental probability describes how often an outcome actually occurs during repeated trials. Instead of relying on what should happen in theory, it uses real data collected from experiments. Dice are frequently used in GCSE Maths questions because they clearly demonstrate randomness while still being simple to understand.

The Core Formula

Experimental probability = number of times the event occurs ÷ total number of trials

This formula always uses observed results. The final value will always lie between 0 and 1 and may be written as a fraction, decimal, or percentage depending on the question.

Worked Example

A die is rolled 60 times and the number 2 appears 11 times. The experimental probability of rolling a 2 is:

\( \frac{11}{60} \)

This probability is based entirely on the results of the experiment, not on the assumption that each number is equally likely.

Experimental vs Theoretical Probability

Theoretical probability assumes all outcomes are equally likely. For a fair die, each number has the same chance. Experimental probability, however, may differ because it depends on what actually happens during the trials.

As the number of trials increases, experimental probability often moves closer to the theoretical probability, but it may not match it exactly.

Why Large Numbers Matter

With a small number of trials, random variation can strongly affect results. Increasing the number of trials usually leads to more reliable results, as chance has less impact.

This is why experiments involving probability often use many repetitions.

Common Mistakes

• Using the number of possible outcomes instead of observed results
• Assuming the answer must match theoretical probability
• Forgetting to simplify the fraction
• Mixing up experimental and theoretical probability

Real-Life Applications

Experimental probability is widely used in real life. Scientists repeat experiments to check reliability. Engineers test components to estimate failure rates. Game developers simulate dice rolls to test fairness.

All of these rely on observed data rather than expectations.

Frequently Asked Questions

Can experimental probability change if more trials are added?
Yes. Adding more trials can change the probability and usually makes it more accurate.

Does experimental probability always equal theoretical probability?
No. It often gets closer with more trials, but differences can remain.

Why do GCSE questions use experimental probability?
Because it tests data handling, fractions, and understanding of randomness.

Study Tip

If a question mentions results that were observed, recorded, or happened out of a certain number of trials, always calculate probability using observed results ÷ total trials.