NetLogo Models Library:
Sample Models/Mathematics/Probability

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Birthdays

Run Birthdays in your browser uses NetLogo 5.0.1 requires Java 5 or higher (system requirements) Note: If you download the NetLogo application, every model in the Models Library (besides the Community Models) is included. If you have trouble running this model in your browser, you may wish to download the application instead.

## WHAT IS IT?

In a room of 23 people, what are the chances that some two of them will have the same birthday?

Make your best guess, then run the model and see how often it happens.

## HOW IT WORKS

Each turtle is randomly assigned a birthday. If a turtle has the same birthday as another turtle in the room, it turns green.

The model doesn't take leap years into account (there are no February 29th birthdays).

## HOW TO USE IT

Press SETUP to initialize the model.

Press GO ONCE to generate a single room full of people.

Press GO to repeatedly generate many rooms full of people. The SUCCESS RATE monitor will show what percentage of those rooms had at least one matching birthday.

## THINGS TO NOTICE

Is the success rate higher or lower than you expected?

## THINGS TO TRY

To try a room with more people in it, edit the view and increase max-pycor.

How many people need to be in the room before the chance of a matching birthday is at least 90%? (Is this higher or lower than you expected?)

Can you work out mathematically what the odds should be? (Hint: start by considering the odds when the number of people is small.)

## EXTENDING THE MODEL

Include leap year birthdays in the list of possibilities.

## NETLOGO FEATURES

This model uses lists a lot, including list primitives such as `map`, `foreach`, `item`, `position`, `sentence`, and `sort-by`. Lists are used mostly to make the model display actual day names, instead of just numbers from 0 to 364. Lists are also used when sorting the turtles by birthday.

## RELATED MODELS

The ProbLab suite of models, in the Mathematics/Probability section, contains many explorations of basic questions about probability and statistics.

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:
- Wilensky, U. (2004). NetLogo Birthdays model. http://ccl.northwestern.edu/netlogo/models/Birthdays. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
- Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2004 Uri Wilensky.


This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

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