Shared birthdays in real classes: a maths EPQ idea
A title to start from
How likely are shared birthdays in real classes, given that births are not spread evenly through the year?
Why it works as an EPQ
The classic answer assumes every day is equally likely. Real birth data let you test whether that matters.
Scope and difficulty
Accessible. Accessible. Calculation, simulation and one real data set.
The maths
Builds on these A Level topics: Probability · Hypothesis testing · Sampling and data.
You would learn:
- Complement counting
- Simulation
- Non-uniform probabilities
One possible plan
- Derive the probability of a shared birthday for n people under the usual assumption.
- Find birth counts by day from official statistics.
- Simulate with the real distribution and compare.
- Judge how much the usual assumption matters, and why.
Pitfalls
- Collecting real birthdays from classmates without consent.
- Too few simulation runs.
Where to start reading
- Office for National Statistics births by day of year
- Search for: birthday problem non-uniform distribution
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All statistics and data ideas · all 93 ideas
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