# P2-21: Exploring the Law of Large Numbers through the Egg Roulette Game in Fathom

### Saturday, May 20th9:45 am – 10:45 am ET

By Amanda Walker and Alex White (Texas State University)

### Information

This lesson incorporates a probability game and computer simulation to explore the Law of Large Numbers and conditional events. Students are shown two video clips from The Late Night show, starring Jimmy Fallon who plays the egg roulette game with celebrities. Two players take turns selecting an egg from a cartoon of 12 dozen eggs in which eggs are hard boiled, four eggs are raw, and the first player to smash two raw eggs on his head loses. The teacher asks students several questions regarding the probability of winning the game when guest of the show takes the first turn. This leads to a discussion of conditional events. Students then play the game in pairs, using beads, and the number of wins for each player is recorded for the class. This gives an empirical probability that Fallon, who takes the second turn, will win the game. (Bready & Bush).

We’ve created a Fathom simulation so students can discover the theoretical probability that Fallon wins the game, which is used to teach the Law of Large Numbers. Participants of the poster session can interact with the fathom simulation displayed on the presenter’s laptop. Fathom is a statistical software that is inexpensive, fun to use, and can be downloaded from the internet. Fathom is a very effective method for visualization of data analysis and sampling. A link to the Fathom file for instructors will be posted on our department’s webpage.

Low tech adaptions: This lesson can be adapted in a low tech classroom by using the Rossman/Chance one proportion applet: http://www.rossmanchance.com/ISIapplets.html

Using the applet involves telling students ahead of time the theoretical probability Fallon wins the game is 5/9. A large number of samples can be taken, using the same sample size as the classroom, and the sampling distribution of proportions can be explored. The applet also allows students to explore the likelihood of obtaining an empirical proportion as or more extreme than what was observed in the class sample.