AQA•GCSE•Mathematics•Probability
Relative frequency
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EasyQuestion 1
[2 marks]A dice is rolled 50 times. It lands on 6 a total of 12 times.
Find the relative frequency of rolling a 6.
Solution for Question 1
MediumQuestion 2
[3 marks]A spinner was spun 200 times with results:
- Red: 45 times
- Blue: 82 times
- Green: 73 times
(a) Estimate the probability of landing on blue.
(b) If the spinner is spun 500 times, estimate how many times it lands on green.
Solution for Question 2
HardQuestion 3
[4 marks]A coin is suspected of being biased. It is flipped 100 times and lands on heads 62 times.
(a) Estimate the probability of heads.
(b) If the coin were fair, how many heads would you expect in 100 flips?
(c) Does the evidence support the coin being biased? Explain.
Solution for Question 3
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Relative frequency (or experimental probability) is calculated from actual results: relative frequency = frequency of outcome / total number of trials. It estimates the theoretical probability when that's unknown or when testing if an item is fair.
As the number of trials increases, relative frequency gets closer to the theoretical probability. This is the Law of Large Numbers. A few trials might give very different results from the true probability; many trials give a better estimate.
To estimate expected outcomes: expected frequency = probability × number of trials. This gives what we'd expect "on average" - actual results will vary.
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