GCSE Maths Practice: theoretical-vs-experimental-probability

Question 3 of 11

This question focuses on finding experimental probability from observed coin flip results.

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\( \begin{array}{l}\text{A coin is flipped 100 times, and it lands tails 45 times.} \\ \text{What is the experimental probability of landing tails?}\end{array} \)

Choose one option:

Always base your calculation on observed outcomes, not on what you expect to happen.

Experimental Probability Using Coin Tosses

Experimental probability is based on results collected from carrying out an experiment rather than from what is theoretically expected. Coin flips are a common and effective way to introduce this idea in GCSE Maths, as they are simple to understand while still showing how randomness works in practice.

The Core Formula

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

This formula is always applied using observed data. The result is usually written as a fraction, but it may also be expressed as a decimal or percentage depending on the question.

Worked Example

Suppose a coin is flipped 80 times and lands heads 38 times. The experimental probability of landing heads is:

\( \frac{38}{80} = \frac{19}{40} \)

This value is found directly from the results of the experiment, not from the assumption that the coin is perfectly fair.

Experimental vs Theoretical Probability

Theoretical probability predicts outcomes based on equally likely results. For a fair coin, the theoretical probability of heads or tails is 1/2. Experimental probability, however, depends on the results collected and may differ from the theoretical value.

As the number of trials increases, experimental probability often gets closer to the theoretical probability, but small differences can still occur due to randomness.

Why Results Are Not Always Exactly 1/2

In real experiments, outcomes are influenced by chance. Short experiments may produce uneven results. Larger numbers of trials usually lead to more balanced results, but perfect balance is not guaranteed.

This is why experimental probability is described as an estimate rather than an exact value.

Common Mistakes

  • Assuming the answer must be 1/2 because a coin is fair
  • Using the number of possible outcomes instead of observed results
  • Failing to simplify the fraction
  • Mixing up experimental and theoretical probability

Real-Life Applications

Experimental probability is used in many real-world situations. Game designers test outcomes by running simulations. Scientists analyse repeated trials to evaluate experiments. Businesses review historical data to estimate future outcomes.

In each case, decisions are made using observed data rather than assumptions alone.

Frequently Asked Questions

Can experimental probability ever be exactly 1/2?
Yes, but it depends on the results. It is possible, but not guaranteed.

Does experimental probability change?
Yes. If more trials are carried out, the probability may increase or decrease.

Why is this topic important for GCSE Maths?
It builds understanding of randomness, fractions, and data interpretation.

Study Tip

If a probability question mentions results that were recorded, observed, or obtained from repeated trials, always calculate experimental probability using results ÷ total trials.

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