May 29, 2013
In probability theory, the central limit theorem (CLT) states that, given certain conditions, the mean of a sufficiently large number of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed.
which is what we see here. at every triangle, the ball has a 50/50 shot of going to the left or to the right. you can also think of it like coin flips, where the number of coin flips is
if we assign heads to 0, and tails, 1 (or 0 for left, 1 for right as in the case of the visualization above)
for 1 coin flip, the possible sums of coin flips are:
0 -> 0 1 -> 1
so for 1 coin flip, there are 2 different possible outcomes, each equally likely. the expected percentage of the possible outcomes is then:
0: 50% 1: 50%
for 2 coin flips, all possible outcomes are:
0 + 0 -> 0 0 + 1 -> 1 1 + 0 -> 1 1 + 1 -> 2
so for 2 coin flips, there's only 3 different possible expected coin sums. But unlike the other outcomes, the outcome where the coins total 1, is possible in two coin combinations so the probability is double in this case. Our expected percentages would then look like:
0: 25% 1: 50% 2: 25%
give it a try!
note: this visualization was inspired by: http://vis.supstat.com/2013/04/bean-machine/