The quincunx is a device invented by Francis Galton in 1889 that illustrates the binomial probability distribution. It looks a bit like this

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Imagine that we are looking face-on at a sloping board. The board has nails hammered into it (indicated by dots here) and we drop steel balls through a small aperture at the top. As the metal ball falls it will strike a nail in the first row. (At least in principle) it has probability 1/2 to fall to the left of the nail it hits and probability 1/2 to fall to the right of it. Now providing we have arranged the nails properly it will strike a nail on the next row and again will fall with equal probablity to the left or right of that nail.

At the bottom of the device are containers to catch the falling metal balls that are just wide enough so that the balls falling in will have to lie on top of one another and not side by side. In this way we can see visually the distribution.

The reason that the distribution is binomial is as follows. On the second row the proportion of outcomes for where the ball will fall (to the left, between the two nails, to the right of the two nails) is 1:2:1. On the next level we get 1:3:3:1 and so on, the familiar lines of Pascal's Triangle.

Galton was interested in this because when the number of nails and balls gets large we get closer and closer to a normal distribution.

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