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 faceon 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.