A coin is flipped 50 times and lands heads 18 times.
- (a)Work out the relative frequency of heads.[1]
- (b)Using this, estimate the number of heads in 400 flips.[1]
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You cannot calculate the probability that a drawing pin lands point up, or that a particular spinner is fair, just by counting outcomes. Instead you experiment: repeat the trial many times and see how often the event happens. That proportion, the , estimates the probability — and the more trials, the better the estimate.
The big picture
Theoretical probability predicts; relative frequency measures. When a coin is flipped 10 times, 7 heads is not unusual, but in 10 000 flips the proportion of heads settles very close to 0.5. That settling down is why larger samples give more reliable estimates, and why Edexcel asks which of several estimates is best.
Expected frequency turns a probability into a prediction: the number of times you would expect an event in a given number of trials. Comparing expected and observed frequencies is how you decide whether a dice or spinner might be biased.
What you'll learn
Relative frequency .
It estimates the probability. Different experiments give different estimates, because results vary randomly.
A spinner lands on blue 81 times in 300 spins. Estimate the probability of blue.
As the number of trials increases, the relative frequency tends to get closer to the true probability.
So when several groups run the same experiment, the best estimate combines all the results, or uses the group with the most trials.
Relative frequency graphs typically fluctuate wildly at first, then level off.
This is the law of large numbers in action. Random variation does not disappear with more trials, but it becomes a smaller proportion of the total, so the estimate stabilises.
Expected frequency probability × number of trials.
It is what you would expect on average; the actual result will usually be close but not exact.
Using the estimate , how many times would you expect blue in 800 spins?
Compare the observed relative frequency with the theoretical probability. A large difference over many trials suggests bias.
Small differences over a few trials are expected by chance, so they are not strong evidence.
Tip — Use cautious language: "probably biased" or "suggests it is biased". An experiment gives evidence, not certainty.
Think like an examiner
Experimental probability
Watch out for these
Stretch yourself
A biased spinner has four colours. After 400 spins the frequencies are red 90, blue 130, green 100, yellow 80. The spinner is spun 60 more times. Estimate how many times it lands on a colour other than blue, and explain how reliable your estimate is.
Hint — Estimate P(not blue) from the 400 spins, then multiply by 60.
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
A coin is flipped 50 times and lands heads 18 times.
Adam does 30 trials and gets 12 successes. Beth does 270 trials and gets 96 successes.
Unlimited practice
A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.
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Test yourself
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Real past-paper questions on Relative Frequency & Expected Outcomes, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.