When a marble is dropped into the pegboard, it will bounce through 10 rows of
pegs. (For those that are counting, there are 11 rows, but the top row does not
affect the path of the marble.) When a marble bounces on a peg, it will fall left 50% of the
time and right 50% of the time. The path of the marble represents 10 trials which each
end in an outcome of left or right, with left and right being equally likely. The final column
that a marble lands in represents how many left (or right) turns the marble took.
If the outcomes of the bounces on each level of the pegboard are independent*
then the path of each marble represents a sampling instance of a binomial random
variable with 10 trials and probability of success 50%. The column that the marble lands in
represents a value of the random variable. As the number of marbles dropped increases,
the counts of marbles in the individual columns will begin to approximate a binomial
distribution.
*The bounces of the marbles are not technically independent.
If the spaces between the pegs are large enough, and if the coefficient of restitution of the
bouncing is high enough, the result of one bounce can dramatically affect the next. With
narrow gaps between the pegs and a lower coefficient of restitution, this dependency can
be diminished somewhat.
