GCSE Maths Practice: theoretical-vs-experimental-probability

Experimental Probability Using Spinners with Multiple Trials

Experimental probability is calculated using data collected from real experiments rather than from predictions. In Higher GCSE Maths, students are expected to analyse experimental results carefully and understand how these results relate to theoretical probability. Spinners with equal sections are commonly used because they provide a clear and visual way to explore randomness.

The Fundamental Formula

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

This formula always relies on observed data. The probability can be written as a fraction, decimal, or percentage depending on the requirements of the question.

Worked Example

A spinner with six equal sections is spun 75 times. The spinner lands on orange 18 times. The experimental probability of landing on orange is:

\( \frac{18}{75} = \frac{6}{25} \)

This value comes directly from the experiment and does not assume that outcomes must be equally balanced.

Experimental vs Theoretical Probability

Theoretical probability is calculated using known information, such as the number of equal sections on a spinner. For a spinner with five equal sections, each colour has the same theoretical probability. Experimental probability, however, depends on observed outcomes and may differ because of randomness.

As the number of spins increases, experimental probability often moves closer to the theoretical probability, but it does not need to match it exactly.

Why Results Vary

Random variation means that short experiments can produce uneven results. Even when many trials are carried out, results may still differ slightly from expectations. Larger sample sizes generally produce more stable results, but chance is never completely removed.

This idea links closely to the law of large numbers, which is an important concept at Higher GCSE level.

Common Mistakes

• Using the number of spinner sections instead of observed results
• Assuming experimental probability must equal theoretical probability
• Forgetting to simplify fractions fully
• Rounding too early during calculations

Real-Life Applications

Experimental probability is widely used outside the classroom. Game designers test spinners and wheels to check fairness. Researchers analyse repeated trials to study behaviour. Businesses examine large sets of data to understand customer choices.

In each case, conclusions are based on observed results rather than assumptions.

Frequently Asked Questions

Does experimental probability always match theoretical probability?
No. It often becomes closer with more trials, but exact matches are rare.

Can experimental probability be written as a decimal?
Yes. Fractions, decimals, and percentages are all acceptable unless stated otherwise.

Why is this a Higher-tier question?
Because it requires interpretation of experimental data rather than simple counting.

Study Tip

Whenever a question mentions observed results or recorded outcomes, always use experimental probability and ignore how many sections the spinner has.