GCSE Maths Practice: theoretical-vs-experimental-probability

Question 1 of 11

This question tests how to calculate experimental probability using observed results from repeated trials.

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\( \begin{array}{l}\text{A bag contains 6 red, 4 blue, and 10 green marbles.} \\ \text{A marble is drawn 40 times, and a red marble is drawn 18 times.} \\ \text{What is the experimental probability of drawing a red marble?}\end{array} \)

Choose one option:

Always form the probability using the results you are given, not the contents of the bag.

Understanding Experimental Probability

Experimental probability is based on what actually happens when an experiment is carried out. Instead of relying on expected outcomes, it looks at real data collected from repeated trials. This makes experimental probability especially useful when results may vary or when the theoretical probability is difficult to calculate.

The Key Idea

The formula for experimental probability is:

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

This method focuses on observation rather than prediction. As more trials are carried out, experimental probability often moves closer to the theoretical probability, but they are not always exactly the same.

Worked Example

Suppose a spinner is spun 50 times, and it lands on blue 22 times. The experimental probability of landing on blue is:

\( \frac{22}{50} = \frac{11}{25} \)

This value comes directly from observed results, not from how the spinner is designed.

Why Experimental Probability Can Change

Experimental probability depends on sample size. If only a few trials are completed, results may vary significantly. As the number of trials increases, the results tend to become more stable and reliable.

For example, flipping a coin 10 times might give 7 heads, but flipping it 1,000 times will usually produce a result much closer to an even split.

Common Mistakes to Avoid

  • Using the total number of possible outcomes instead of observed trials
  • Forgetting to simplify the fraction
  • Confusing experimental probability with theoretical probability
  • Including outcomes that are not relevant to the event being measured

Real-Life Applications

Experimental probability is widely used in real-life situations. Weather forecasting uses historical data to estimate the chance of rain. Sports analysts examine past performances to estimate the likelihood of winning. Quality control in factories uses experimental probability to estimate defect rates.

In each case, decisions are made using observed data rather than perfect theoretical models.

Frequently Asked Questions

Does experimental probability always match theoretical probability?
Not always. They become closer with more trials, but randomness can still cause variation.

Can experimental probability be greater than 1?
No. Since it is a fraction of occurrences over trials, it must always be between 0 and 1.

Why do exam questions use experimental probability?
Because it tests understanding of data handling, fractions, and interpretation of results.

Study Tip

Whenever you see the words observed, recorded, or out of in a GCSE Maths probability question, think experimental probability and immediately look for the fraction formed from results ÷ trials.

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