10182

# An Increasing Preference Distribution

Suppose your music player contained songs and you set it to shuffle songs, giving increasing preference to a song each time it was played. That is, initially, all songs are equally likely to be chosen but every time a song is played, its probability of being selected for the next play goes up in such a way that the probability of it being selected is proportional to the number of times it has been played. What would happen over a large number of plays? Would all your songs remain about equally likely or would a few dominant favorites emerge? Investigate this using this Demonstration.

### DETAILS

If there are songs, then for the first selection, each song is given equal probability . If song is selected for the first play, then song has probability of being selected for the second play while all other songs have probability of being selected. After plays, suppose the song has been played times. Then for the play, it has probability of being selected.

### 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 Curriculum Standards

US Common Core State Standards, Mathematics

 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.
 © 2015 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS
 Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX Download or upgrade to Mathematica Player 7EX I already have Mathematica Player or Mathematica 7+