Statistics and Probability · Probability
Test the birthday paradox
Calculate and test the chance that two people in a group share a birthday.
- DifficultyEasy
- Estimated time1–3 hours
- Budget₹0
- ClassClass 9–12
- TeamSolo or up to 2
- You needNo equipment
Prerequisites: None beyond your class work
Original · by TechnifyedExperimentSimulationBeginner friendlyFree to doNo equipmentWell documented
Overview
Calculate and test the chance that two people in a group share a birthday.
Why build this?
The answer surprises almost everyone, and you can confirm it with your own school's classes.
What you will learn
- How to calculate a probability through its complement
- Why pairs grow faster than people
- How simulation supports theory
Skills you will use
Safety
- This project handles personal data. Collect the minimum, store it safely, get permission, and delete it when the project ends.
Materials and tools
- Birthday lists for several classes (day and month only)
- Calculator or spreadsheet
Tools and software
Step-by-step roadmap
Start
You will finish with: a probability table for group sizes 5 to 60 and your test results.
- 1
Prerequisites
Nothing special to know first. Then collect the 2 items in the materials list.
- 2
Learn
- How to calculate a probability through its complement
- Why pairs grow faster than people
- How simulation supports theory
- 3
Plan
Write your question, your hypothesis and the one thing you will change. Draw the table you will fill in before you start.
- 4
Build
- Calculate the probability of a shared birthday for 23 people.
- Collect day-and-month birthdays from five classes.
- Record which classes have a match.
- Simulate 1,000 random groups in a spreadsheet.
- Compare theory, simulation and real classes.
- 5
Test
Repeat every reading at least three times and check the result against what the science predicts.
- 6
Document
Record every reading with its unit, photograph the setup and draw a graph of the result. Report structure
- 7
Present
Explain the question, the method and the graph in two minutes; keep the setup ready to demonstrate. Presentation structure · Viva questions
- 8
Publish
Share the report and photos with your class, a science fair or your school magazine.
Expected outcome
A probability table for group sizes 5 to 60 and your test results.
Other versions of this project
Beginner version
Check five classes for a shared birthday.
Advanced version
Find the group size for a 50 percent chance of three people sharing.
Make this project better
- BasicCheck five classes for a shared birthday.
- This projectTest the birthday paradox
- AdvancedFind the group size for a 50 percent chance of three people sharing.
Science fair mode
Text marked "You write this" is a prompt for your own work; everything else is specific to this project.
- Problem
- You write thisWrite your question as: How does [what you change] affect [what you measure]?
- Hypothesis
- You write thisWrite it as: If [I change this], then [this will happen], because [reason].
- Variables
- You write thisName the one thing you change (independent), the thing you measure (dependent) and what you keep the same (controlled).
Materials and procedure are in Materials and the Roadmap.
Observation table
You write thisDraw a table with one column for what you change, one for each repeat reading and one for the average.
- Graph
- You write thisPlot what you changed along the bottom and what you measured up the side; use a bar chart for categories and a line graph for numbers.
- Results
- You write thisState what the graph shows in one or two sentences, with numbers.
- Conclusion
- You write thisSay whether the result supports your hypothesis and why you think so.
Display board
- Title and your name
- Question
- Hypothesis
- Materials
- Procedure (with photos)
- Data table and graph
- Conclusion
- What you would do next
Questions judges ask
- How many people give a 50 percent chance of a match?
- Why is it so few?
- Why calculate the chance of no match first?
- What would you change if you did this again?
- What was your biggest source of error, and how did you reduce it?
- Where is this idea used in real life?
Working as a team
Solo or up to 2. Suggested roles:
Report and presentation
Report structure
- Title and question
- Background: the science behind it
- Hypothesis
- Materials
- Method (steps, with a diagram or photo)
- Observations (table)
- Results (graph and calculation)
- Sources of error
- Conclusion
- What you would do next
- References
Presentation structure
- The question
- Why it matters
- The idea behind it
- Setup (photo)
- Method in three steps
- Results (one clear graph)
- What the result means
- Errors and limits
- Conclusion and next step
Viva questions
Try answering before you open each one.
How many people give a 50 percent chance of a match?
Twenty-three.
Why is it so few?
With 23 people there are 253 possible pairs.
Why calculate the chance of no match first?
It is simpler, and the answer is one minus that.
Resources
Decision making with spreadsheetIIT Roorkee · Free course course
33 Spreadsheet Projects Course for Beginners – Excel and Google SheetsfreeCodeCamp · Free video course
Analyzing Spreadsheet Data with PythonIBM · Free course courseLibreOfficelibreoffice.orgKhan Academykhanacademy.orgOpen Government Data Platform Indiadata.gov.inSource and attribution
Original
Written by Technifyed. Free to use for your own school or college project; write the report in your own words. Added 1 Oct 2026.
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