10176

# Binomial Approximation to a Hypergeometric Random Variable

If balls are sampled from a bin containing balls of which are marked, then the distribution of the number of marked balls in the sample depends on whether the sampling is done with or without replacement.
If the sampling is done with replacement, the number of marked balls is a binomial random variable, while if the sampling is done without replacement, then this quantity is a hypergeometric random variable. However, if the number of balls sampled is small relative to the number of balls in the bin, it makes little difference how the sampling is done.
The probability histogram for the binomial random variable is colored orange, and the hypergeometric random variable is blue. A measure of agreement between the two is obtained by computing the purple area—100% would represent complete agreement between the two distributions.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.