GCSE Maths Practice: theoretical-vs-experimental-probability

Experimental Probability Using Spinners with Many Sections

Experimental probability is calculated using data collected from real experiments rather than from predictions. In Higher GCSE Maths, students are expected to interpret experimental results carefully and understand how these results compare with theoretical probability. Spinners with many sections provide a useful way to explore this idea, as they often highlight differences between expected and observed outcomes.

The Fundamental Formula

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

This formula always uses observed data. The final probability can be written as a fraction, decimal, or percentage depending on what the question asks.

Worked Example

A spinner with ten equal sections is spun 40 times. It lands on orange 7 times. The experimental probability of landing on orange is:

\( \frac{7}{40} \)

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

Experimental vs Theoretical Probability

Theoretical probability is calculated using known information, such as the number of sections on a spinner. For a spinner with eight equal sections, each colour has the same theoretical probability. Experimental probability, however, depends on what actually happens during the experiment and may differ because of randomness.

As the number of spins increases, experimental probability often moves closer to the theoretical probability, but exact matches are not guaranteed.

Why Results Can Differ

Random variation plays a major role in experimental probability, especially when the number of trials is relatively small. With only a limited number of spins, some outcomes may appear more or less often than expected. Increasing the number of trials usually makes the results more stable, but variation never disappears completely.

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 match theoretical probability
• Forgetting to simplify fractions fully
• Rounding too early when converting to decimals

Real-Life Applications

Experimental probability is widely used outside the classroom. Game designers test spinners and wheels to ensure fairness. Researchers analyse repeated trials to study patterns of behaviour. Businesses use collected data to understand customer choices and trends.

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

Frequently Asked Questions

Does experimental probability always get closer to theoretical probability?
It usually does as the number of trials increases, but exact equality is rare.

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

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

Study Tip

Whenever a question gives observed results, ignore how many sections the spinner has and focus only on the recorded outcomes.