## Are You Better Than Average?™

*The following has nothing to do with airline safety, but it may help to teach some basic facts about probability and statistics.*

__History of the Game__: Once upon a time, there was a procrastinating dad who promised to make up a game for the math class during Parents Night at his kid's school.
The night before, dad thought "What can I come up with really, really quickly?"
Spying a pair of dice, he thought for a bit and came up with a way to quickly demonstrate some of the basics of probability.
The game does this in a fun way that both kids and adults can enjoy.
The children of Lake Woebegone, who are all above average, inspired the game's title.

__Purpose of the Game__:

To demonstrate three basic principles of applied mathematics: averages, probability, and modeling.

__Materials:__One pair of dice, throwing tray or other flat surface, score sheet (optional)

__About Dice__: A single die has six sides numbered one through six.
With a pair of dice, there are thirty-six possible combinations.
Twelve combinations result in either a double or in two numbers that add up to seven,
therefore there is a 12 in 36 chance, or one in three probability of rolling a double or a seven.

__The Model__: On average, it takes three tries to get either a seven or a double,
therefore if one gets a seven or a double on the first or the second throw, one is better than average.
It can be shown that the probability of getting a double or seven on the first throw
is 1/3 (about 33.3%), the probability of getting it on the second throw is (2/3)x(1/3)= 2/9 (about 22.2%),
and the probability of getting it after two throws is 1-(1/3)-(2/9)= 4/9 (about 44.4%).

This model can be demonstrated by playing the game 99 times - there should be about 33 (1/3 x 99) who get a double or a seven on the first try, 22 on the second try (2/9 x 99), and 44 who do not do so after the first two tries (4/9 x 99). One can keep track of the results by using a three-column score sheet of the results (first throw, second throw, more than two throws).

__Playing the Game__:

- Have someone throw a pair of dice into the throwing tray.
- If the person gets a double or a seven on the first throw, add an "X" in the "Wins on First Roll" table of the score sheet and go to the next player. If the person does not get a double or a seven, throw again.
- · If the person gets a double or a seven on the second throw, add an "X" in the "Wins on Second Roll" table of the score sheet. If the person does not get a double or a seven, add an "X" to the "Loses on Second Roll" table. In either case, move to the next player.
- After 99 players (a person can play more than once), count up the number in each column and see how close it comes to the prediction of the model.
- Remember to keep the atmosphere light and playful!

Download the instructions and a score sheet.

Please feel free to send comments on how well this exercise works. For reprint requests or other copyright and trademark related matters, please contact Todd Curtis.

http://airsafe.com/analyze/average.htm -- Revised: 10 September 2007