Simulation
Revise Simulation for GCSE Statistics with this free worksheet and full mark scheme — Higher tier exam-style questions with worked answers for AQA and Edexcel. Simulation uses random numbers to model and investigate real situations that involve chance.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.
This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.
Topic overview
Simulation uses random numbers to model a real situation, allowing probabilities to be estimated when theoretical calculation is difficult or impossible. This is a Higher-only topic.
Random numbers are assigned to outcomes in proportion to their probabilities. For an event with probability 0.3, the digits 0, 1 and 2 out of 0 to 9 would represent it occurring, and 3 to 9 would represent it not occurring.
The simulation is then run many times and the relative frequency calculated. More runs give a more reliable estimate, for exactly the same reason as with any experimental probability. Simulation is valuable where the real situation would be too slow, too expensive or too dangerous to test directly.
Revision notes
Assigning random numbers
Assign numbers to outcomes in proportion to their probabilities.
For a probability of 0.3 using digits 0 to 9, allocate three digits such as 0, 1 and 2 to that outcome. The proportion of digits must match the probability exactly.
Running the simulation
Generate random numbers and record the outcome each represents.
Repeat many times, then calculate the relative frequency of the event of interest. This estimates the probability without needing a theoretical calculation.
Why simulate
Some situations are too complex to calculate theoretically.
Others would be too slow, too expensive or too dangerous to test in reality. As with any experimental probability, more runs give a more reliable estimate.
Key points
- Simulation models a situation with random numbers.
- Numbers are assigned in proportion to probabilities.
- The simulation is run many times.
- Relative frequency estimates the probability.
- More runs give a more reliable estimate.
- It suits situations too complex to calculate.
Worked examples
Example 1
An event has probability 0.4. Work out how many digits from 0 to 9 should represent it. [2 marks]
Working
Example 2
A simulation of 500 runs gives the event 160 times. Estimate its probability. [2 marks]
Working
Example 3
Explain why a simulation should be run many times. [2 marks]
Working
Common mistakes
Assigning digits out of proportion to the probability.
The proportion of digits must match the probability.
Running too few simulations.
The estimate is unreliable without many runs.
Treating the result as an exact probability.
It is an estimate from relative frequency.
Reusing the same random numbers.
Each run needs fresh random numbers to be independent.
Exam tips
- Multiply the probability by the number of digits available.
- Run the simulation many times.
- Describe the result as an estimate.
- Remember this is a Higher-only topic.
Key terms
- Simulation
- Modelling a situation using random numbers.
- Random number
- A number with no pattern, used to select outcomes.
- Relative frequency
- The proportion of runs giving the event.
- Estimate
- An approximate value from simulation rather than theory.
Related topics
Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.