David Little  
Mathematics Department Penn State University Eberly College of Science University Park, PA 16802 
Office: 403 McAllister Phone: (814) 8653329 Fax: (814) 8653735 email:dlittle@psu.edu 



Plinko and the Binomial Distribution
A Bernoulli trial is an experiment that results in a success with probability p and a failure with probability 1p. 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 1p. 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 offline viewing (includes source code) 