Statistics and data · Accessible · Dissertation

Is the lottery a fair game?: a maths EPQ idea

Why it works as an EPQ

Counting, expected value and hypothesis testing on published results, with a clear conclusion.

Scope and difficulty

Accessible. Accessible. Use the operator's published rules and results; do not buy tickets for the project.

The maths

Builds on these A Level topics: Probability · Statistical distributions · Hypothesis testing.

You would learn:

• Combinations
• Expected value with rollovers
• Testing uniformity of draws

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Calculate the probability of each prize tier from the published rules.
2. Work out the expected value of a ticket, with and without rollovers.
3. Test published results for uniformity.
4. Judge 'fair' in two senses: random, and good value.

Pitfalls

• Prize rules that are out of date.
• Confusing 'random' with 'fair value'.

Where to start reading

• The lottery operator's published game rules and results
• Search for: lottery expected value rollover

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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