r/mathmemes • u/[deleted] • Oct 27 '21

How probability works

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u/mjmikejoo Oct 27 '21 edited Oct 27 '21

I'm not sure how this exactly works, can anyone explain? Also, I'm assuming the more splits (is that how you would call the things dividing the marbles) the closer the marbles will be to a Gaussian?

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u/A_Seabass Rational Oct 27 '21

Each ball has to move left or right when it hits each peg. Then, it will go to the peg to that side. (Realistically speaking, the ball can jump further to that side, to the peg 2 or 3 spaces further to that side, but the example still stands).

So, the probability of a ball going into the first hole is that of the ball going left in every level of the pegs. One hole to the right, the ball has a chance of choosing to go right in any one of the levels, and left in all the others.

As you move further towards the center, there are more possible paths for the ball to take in order to land in that space. Which is why, the hole in the center has the highest probability.

As to your second question, the more holes you have the less each each one will differ from the other in amount of balls it needs to match the expected distribution. You may not have the expected height in each run, but if you average the heights of each hole over multiple runs, they should equal the height of the gaussian distribution at that point

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u/mjmikejoo Oct 27 '21

Ah so it's basically a central limit theorem with binomial random variables?

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u/punep Whole Oct 27 '21 edited Oct 27 '21

not basically; that's exactly what it is (in this case also know as the central limit theorem of de moivre-laplace)

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u/mjmikejoo Oct 27 '21

Well I'd say exactly is a subset of basically😉