GCSE Maths Practice: theoretical-vs-experimental-probability

Question 10 of 11

This question focuses on calculating experimental probability using results from repeated spins of a multi-colour spinner.

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\( \begin{array}{l}\text{A spinner has 5 equal sections: red, blue, green, yellow, purple.} \\ \text{It lands on green 8 times in 20 spins. What is the experimental probability?}\end{array} \)

Choose one option:

Always calculate experimental probability using observed results rather than expected outcomes.

Experimental Probability Using Multi-Colour Spinners

Experimental probability focuses on results collected from carrying out an experiment rather than on what is expected to happen. In GCSE Maths, spinners are often used because they provide clear outcomes and help students see how randomness works in practice.

The Core Idea

To find experimental probability, use the formula:

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

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

Worked Example

A spinner with six equal sections is spun 30 times and lands on orange 11 times. The experimental probability of landing on orange is:

\( \frac{11}{30} \)

This value comes directly from the results of the experiment, not from how many sections the spinner has.

Experimental vs Theoretical Probability

Theoretical probability is calculated using known information, such as the number of equal sections on a spinner. If a spinner has five equal sections, each colour has the same theoretical chance. Experimental probability, however, is based on what actually happens and may differ due to randomness.

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

Why Results Can Be Uneven

When only a small number of spins are carried out, results may be uneven because of chance. Increasing the number of spins usually makes the results more reliable, as random variation has less impact.

This is why probability experiments often involve many repeated trials.

Common Mistakes

  • Using the number of sections on the spinner instead of observed results
  • Assuming results must match theoretical probability
  • Forgetting to simplify fractions
  • Confusing experimental probability with theoretical probability

Real-Life Applications

Experimental probability is widely used in everyday life. Game designers test spinners and wheels to ensure fairness. Scientists repeat experiments to check reliability. Businesses analyse customer behaviour using collected data.

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

Frequently Asked Questions

Can experimental probability change?
Yes. Adding more trials can change the probability and usually improves accuracy.

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

Why are spinners used in GCSE Maths questions?
Because they clearly demonstrate randomness and repeated trials.

Study Tip

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

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