David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Plinko and the Binomial Distribution
A Bernoulli trial is an experiment that results in a success with probability p and a failure with probability 1-p. A random variable is said to have a Binomial Distribution if it is the result of recording the number of successes in n independent Bernoulli trials.

In the Applet below, we have represented repeated independent Bernoulli trials by a single ball falling through an array of pins. Each time a ball falls onto a pin, it will bounce to the right (i.e. a success) with probability p or to the left (i.e. a failure) with probability 1-p. After the ball falls through the array, it lands in a bin labeled by the corresponding number of successes.

Click on a bin to see its corresponding total and probability. Alternatively, use the left and right arrow buttons to scroll through the bins. Also displayed is a confidence interval centered on the theoretical expected bin. Bins that are included in this confidence interval are highlighted in green.

* The name Plinko refers to a game played on The Price Is Right. However, the game show version is played on a rectangular array of pins instead of a triangular array. It would be more appropriate to call our applet Galton's board or a quincunx board, however this is far more difficult to pronounce.


© 2004 David P. Little
Download this applet for off-line viewing (includes source code)