10178

This Demonstration of the birthday problem shows the probability that at least two individuals share the same birthday assuming that there are 365 equally likely possible birthdays.
You may be surprised to find that if you randomly select 23 people there is just over a 50% probability that at least two of the individuals will share the same birthday. Move the slider to add more people and see how the probability increases. At around 57 people you should find the probability of a match reaches approximately 99%.

### DETAILS

The formula for the probability of at least two people out of to share the same birthday is:
, where is a binomial coefficient.
Reference
[1] E. H. McKinney, "Generalized Birthday Problem," The American Mathematical Monthly, 73(4), 1966 pp. 385–387.

### 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.