9804

The Birthday Problem and Some Generalizations

The birthday problem asks, "How many randomly selected people must there be in a room in order for the probability that two people share a birthday to exceed 0.5?" and has the well-known answer 23. The following generalizations are illustrated here, along with answers:
1. The probability of 0.5 can be replaced by any value from 0.01 to 0.99, in increments of 0.01.
2. The number of days in a year can be any value from 2 through 5000, for the convenience of extraterrestrials.
3. The question "How many randomly selected people must there be in a room in order for the probability that two people share a birthday or have birthdays on consecutive days to exceed 0.5?" is investigated.
Any combination of these generalizations can be used simultaneously.
  • Contributed by: Marc Brodie (Wheeling Jesuit University)

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • 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 »

Files require Wolfram CDF Player or Mathematica.







Related Curriculum Standards

US Common Core State Standards, Mathematics



 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
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+