Chances Are

A large blue rectangular exhibit with a glassed area to the left and a monitor to the right.

Pascal's triangle and the Law of Large Numbers allow a confident prediction of where a ball will land as it falls through a series of pegs.

How it works

Drop a ball through a series of pegs that are arranged in Pascal’s triangle formation and watch where the ball lands at the base. Check a distribution graph on the screen to see the pattern of where each ball has travelled and landed over time (since 2012).

Things to try or ask around the exhibit

  • Can you predict where the ball will land?
  • What patterns can you find in the numbers printed on the pegs?
  • Can you see a trend in where the ball lands from results on the screen?
  • Why do the balls tend to land in the same spot?

Background

The numbers on the pegs represent Pascal’s triangle. Any two pegs that are next to each other total the number on the peg in the line underneath them. This number tells you how many ways a ball can reach that peg.

The Law of Large Numbers says that collecting more experimental data (for example, dropping many balls), means the actual results get closer to the theoretical, expected results. If you drop only one ball, it would be unexpected for it to land in the corners of the triangle. If you drop thousands of balls, you would expect a few to land in the corners of the triangle.