Galton's Board or Quincunx

This applet simulates Galton's Board, in which balls are dropped through a triangular array of nails. This device is also called a quincunx . Every time a ball hits a nail it has a probability of 50 percent to fall to the left of the nail and a probability of 50 percent to fall to the right of the nail.

The piles of balls which accumulate in the slots beneath the triangle will resemble a binomial distribution. To reach the bin at the far left the ball must fall to the left every time it hits a nail.

Because Galton's board consists of a series of experiments the piles in the slots are the sum of 10 random variables. Therefore, this simulation provides also an illustration of the central-limit theorem , which states that the distribution of the sum of n random variables approaches the normal distribution when n is large. When we add more rows of nails to the board the approximation would be better.