Sheet № 187 · Foundation + Higher · AQA · Edexcel · OCR
Expected Frequency –
Expected frequency is a straightforward but important probability topic that appears on both Foundation and Higher GCSE Maths papers across AQA, Edexcel and OCR. It links theoretical probability with real-world experiments by predicting how often an event should occur over a number of trials. You also need to compare expected frequencies
§Key definitions
Question:
A fair spinner has 5 equal sections coloured red, blue, green, yellow and white. The spinner is spun 200 times. How many times would you expect it to land on blue?
Answer:
You would expect it to land on blue 40 times.
(a)
Expected heads = 0.6 x 250 = 150.
Q1 (Foundation):
A fair dice is rolled 180 times. How many times would you expect to roll a 3?
Q2 (Foundation):
The probability of it raining on any given day is 0.3. In a 30-day month, how many rainy days would you expect?
§Formulas to memorise
Expected frequency = Probability of the event x Number of trials
Multiply: expected frequency = probability x number of trials.
P(blue) = 1/5 = 0.2.
Expected frequency = 0.2 x 200 = 40 times.
Worked example
A fair spinner has 5 equal sections coloured red, blue, green, yellow and white. The spinner is spun 200 times. How many times would you expect it to land on blue?
Working:
⚠ Common mistakes
- ✗Expecting exact results. Expected frequency is a prediction, not a guarantee. Actual results will vary due to chance.
- ✗Concluding bias from few trials. A small number of trials can produce large deviations by chance. Always mention sample size when discussing fairness.
- ✗Forgetting to multiply. Some students state the probability as the answer instead of multiplying by the number of trials.
✦ Exam tips
- →Expected frequency questions are quick marks — just multiply probability by number of trials.
- →If asked "Is the dice/coin/spinner fair?", compare actual frequencies with expected and comment on whether differences are within reasonable variation.
- →Always state that more trials would give more reliable conclusions when evaluating fairness.
- →For related topics, see relative frequency and probability scale and basic probability. For key formulas, visit our GCSE Maths formulas page.