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Frequency of Outcomes in a Small Number of Trials

Difficulty
Time Required Very Short (≤ 1 day)
Prerequisites None
Material Availability Readily Available
Cost Very Low (under $20)

Abstract

People often draw conclusions from a small number of observations, but how easy is it to draw the wrong conclusion? Here is a simple project that shows the importance of making enough observations before making a prediction.

Objective

The objective of this project is to determine what happens when a test with two equally-likely outcomes is performed only a small number of times.

Credits

Gabriel Desjardins

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Last edit date: 2013-01-10

Introduction

A lot of times, people use very small sample sizes to evaluate the likelihood of an event taking place. But does the most likely outcome occur if an experiment is only performed a few times? How easy is it to draw the wrong conclusion if an unlikely event occurs?

Terms and Concepts

Bernoulli trials

Bibliography

http://www.math.wichita.edu/history/topics/probability.html#bern-trials

Experimental Procedure

  • Get any coin. Flip it three times. Record the results. Repeat twenty times.
  • Flip it five times and record the results. Repeat this twenty times.
  • Then flip it seven times, recording the results. Repeat twenty times.
  • What are the most common sequences that result? Did you ever get an unlikely sequence? How does the result change as you flip three, five or seven times?

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Variations

Show, using Bernoulli trials, what the likelihood of each outcome is.

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