GCSE Maths Practice: theoretical-vs-experimental-probability

Question 2 of 11

This question focuses on calculating experimental probability from observed results.

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\( \begin{array}{l}\text{A bag contains 8 red, 3 blue, and 9 green marbles.} \\ \text{A marble is drawn 60 times, and a blue marble is drawn 12 times.} \\ \text{What is the experimental probability of drawing a blue marble?}\end{array} \)

Choose one option:

Always base experimental probability on what actually happened, not on what was expected.

What Is Experimental Probability?

Experimental probability is based on real results collected from carrying out an experiment. Instead of predicting what should happen, it measures what actually happened. This type of probability is commonly used in GCSE Maths questions that involve repeated trials, observations, or recorded outcomes.

The key idea is simple: count how many times an event happens and compare it to the total number of attempts.

The Formula

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

This formula always produces a value between 0 and 1, since the event cannot occur more times than the number of trials.

Worked Example

Imagine a dice is rolled 30 times and a six appears 9 times. The experimental probability of rolling a six is:

\( \frac{9}{30} = \frac{3}{10} \)

This probability comes entirely from the observed results, not from what we expect based on the dice being fair.

Experimental vs Theoretical Probability

Theoretical probability is calculated using known outcomes, such as the number of sides on a dice or the colours in a bag. Experimental probability, however, relies on data collected through testing.

When an experiment is repeated many times, the experimental probability often gets closer to the theoretical probability. However, they may not be exactly the same due to randomness.

Why Results Can Vary

Experimental probability can change depending on the number of trials. With only a small number of trials, results may be uneven. Increasing the number of trials usually makes the probability more reliable.

For example, flipping a coin 5 times may give unexpected results, while flipping it 500 times is more likely to give a balanced outcome.

Common Mistakes

  • Using the total number of possible outcomes instead of the number of trials
  • Forgetting to simplify the fraction
  • Mixing up experimental and theoretical probability
  • Including outcomes that are not relevant to the event

Real-Life Uses

Experimental probability is widely used in everyday life. Scientists use repeated experiments to test hypotheses. Sports analysts examine past match results to estimate winning chances. Manufacturers test products to estimate fault rates.

In all of these cases, decisions are based on collected data rather than assumptions.

Frequently Asked Questions

Can experimental probability change?
Yes. If more trials are carried out, the probability may increase or decrease depending on the results.

Does experimental probability have to be a fraction?
No. It can also be written as a decimal or percentage, depending on the question.

Why is this topic important for GCSE Maths?
It develops skills in data handling, fractions, and interpreting results.

Study Tip

When a question includes phrases like observed, recorded, or out of, it is a strong signal that you should calculate experimental probability using results ÷ trials.

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