AQA•GCSE•Mathematics•Probability
Expected frequency
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EasyQuestion 1
[2 marks]A fair dice is rolled 120 times.
How many times would you expect to roll a 3?
Solution for Question 1
MediumQuestion 2
[3 marks]A biased coin has P(heads) = 0.65.
The coin is flipped 200 times.
(a) How many heads would you expect?
(b) How many tails would you expect?
Solution for Question 2
HardQuestion 3
[4 marks]A spinner has 4 equal sections: A, B, C, D.
Anna spins it 80 times with results:
A: 25, B: 15, C: 18, D: 22
(a) What is the expected frequency for each section if the spinner is fair?
(b) Which section is most likely to be over-represented on the spinner? Explain.
Solution for Question 3
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Expected frequency predicts how many times an outcome should occur based on probability. The formula is: Expected frequency = Probability × Number of trials. This gives the theoretical average, not a guarantee.
For example, if P(6) = 1/6 and you roll a dice 60 times, expected sixes = 1/6 × 60 = 10. You might get 8 or 12, but 10 is the expected average over many repetitions.
Expected frequency questions often ask you to work backwards: given results, assess if they match expectations. Large differences suggest the item might not be fair, but small differences are normal random variation.
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