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Project Summary
| Difficulty | 4 |
| Time required | Very Short (a day or less) |
| Prerequisites | None |
| Material Availability | Readily Available |
| Cost | Very Low (under $20) |
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Sponsor
| Sponsored by a generous grant from Motorola |
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Abstract
This project shows how mathematical probability sometimes contradicts our intuition. Despite the fact that there are 365 days in a year, if you survey a random group of just 23 people there is a 50:50 chance that two of them will have the same birthday. Don't believe it? Try this project and see for yourself.Objective
The objective of this project is to prove whether or not the birthday paradox holds true by looking at random groups of 23 or more people.
Introduction
The Birthday Paradox states that in a random gathering of 23 people, there is a 50% chance that two people will have the same birthday. Is this really true?
Terms, Concepts and Questions to Start Background Research
Birthday Paradox, probability theory, converse probability
Bibliography
There are a number of different sites that explain the Birthday Paradox and explain the statistics. Here is one to get you started:
http://en.wikipedia.org/wiki/Birthday_paradox
Experimental Procedure
1) First you will need to collect birth dates for random groups of 23 or more people. Ideally you would like to get 10-12 groups of 23 or more people so you have enough different groups to compare. Here are a couple of ways that you can find a number of randomly grouped people.
- Most schools have around 25 students in a class, so ask a teacher from each grade at your school to pass a list around each of his/her classes to collect the birth dates for students in each of his/her classes.
- Use the birth dates of players on major league baseball teams. (Note: this information can easily be found on the internet).
2) Next you will need to sort through all the birth dates you have collected and see if the Birthday Paradox holds true for the random groups of people you collected. How many of your groups have two or more people with the same birthday? Based on the birthday paradox, how many groups would you expect to find that have two people with the same birthday?
Variations
- For more science project ideas in this area of science, see Pure Mathematics Project Ideas.
Last edit date: 2005-08-31 15:09:02
Career Focus
If you like this project, you might enjoy exploring careers in Pure Mathematics.
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Statistician Statisticians use the power of math and probability theory to answer questions that affect the lives of millions of people. They tell educators which teaching method works best, tell policy-makers what levels of pesticides are acceptable in fresh fruit, tell doctors which treatment works best, tell builders which type of paint is the most durable. They are employed in virtually every type of industry imaginable, from engineering, manufacturing, and medicine to animal science, food production, transportation, and education. Everybody needs a statistician! |
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