GCSE Maths Practice: theoretical-vs-experimental-probability

Question 11 of 11

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

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\( \begin{array}{l}\text{A spinner has 6 equal sections: red, blue, green, yellow, purple, black.} \\ \text{It lands on blue 9 times in 30 spins. What is the experimental probability?}\end{array} \)

Choose one option:

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

Experimental Probability Using Six-Section Spinners

Experimental probability focuses on what actually happens when an experiment is carried out. Instead of predicting outcomes using theory, it relies on results collected from repeated trials. Spinners with multiple equal sections are frequently used in GCSE Maths to help students understand randomness and relative frequency.

The Key Formula

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

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

Worked Example

A spinner with eight equal sections is spun 40 times and lands on orange 13 times. The experimental probability of landing on orange is:

\( \frac{13}{40} \)

This value is based entirely on observed results rather than the number of sections on the spinner.

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 six equal sections, each colour has the same theoretical chance. Experimental probability, however, depends 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 match it exactly.

Why Results Can Vary

Random variation means that short experiments may produce uneven results. Increasing the number of spins usually makes the results more reliable, as chance has less effect.

This is why probability experiments often involve many repeated trials.

Common Mistakes

  • Using the number of sections on the spinner instead of observed outcomes
  • 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 real-world contexts. Game designers test spinners and wheels to ensure fairness. Scientists repeat experiments to check reliability. Businesses analyse customer behaviour using collected data.

In all cases, decisions are based on observed results 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 small differences can remain.

Why are spinners commonly used in GCSE probability?
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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