GCSE Maths Practice: theoretical-vs-experimental-probability

Question 9 of 11

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

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\( \begin{array}{l}\text{A spinner has 4 equal sections: red, blue, green, and yellow.} \\ \text{It lands on red 12 times in 40 spins. What is the experimental probability?}\end{array} \)

Choose one option:

Always base experimental probability on observed results rather than expected outcomes.

Experimental Probability Using a Spinner

Experimental probability is based on what actually happens when an experiment is carried out. Instead of predicting outcomes using theory, it uses results collected from repeated trials. Spinners are commonly used in GCSE Maths because they clearly show how randomness affects outcomes, even when all sections appear equal.

The Key Formula

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

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

Worked Example

A spinner is spun 50 times and lands on blue 17 times. The experimental probability of landing on blue is:

\( \frac{17}{50} \)

This value comes directly from the experiment and does not depend on 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 four equal sections, each colour has the same theoretical chance. Experimental probability, however, depends on observed results 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 match it exactly.

Why Results May Vary

Random variation means that short experiments can produce uneven results. Increasing the number of trials usually makes the results more reliable, as chance has less influence.

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 situations. Game designers test spinners and wheels to check fairness. Scientists repeat experiments to check reliability. Businesses analyse customer behaviour using historical data.

All of these rely on observed outcomes rather than assumptions alone.

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 small differences can remain.

Why are spinners used in GCSE probability 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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