I understand that at least but I have a question of my own. It's just most likely to form a bell curve, or something close to one. I should point out, though, that it won't always be a perfect bell curve, each run can end up in any state. If you draw that, and work out the probabilities for each position (you only need to be able to divide by 2, and add), you'll get numbers that, drawn on a graph, would form the curve. The pegs one row further in, could have gone, say, LLLR, or RLLL, and whichever other paths, to have arrived there. The pegs on the far left and right, though, only have one parent, so are much less likely.
#Galton board video plus
And from there, it can go two ways, so it's children inherit half the chances of it's leftmost parent, plus half the chances of it's rightmost parent. At each row, the probabilities add up to 100% since it HAS to be somewhere! Each position's odds are those of it's two parents added together. But then the middle channel had a 50% chance, so the two options below it are 37.5% and 37.5% (50 + 25 / 2), compared to the 12.5% of their outer siblings. Then for the next row, it's 25% chance of getting there is split into two for which way it goes next, 12.5%. So the odds for the middle space are 50%. But of the latter two, left then right, or right then left, both will lead to the middle, the same place. To go right, then left, is 25%, and left, then right, is 25%. A 25% chance of it falling right off the first peg, then right off the second. For the first pin, the chances are 50% left, 50% right, right? For the second row, with 2 pins, there's a 25% chance of it falling left off the first peg, then left off the second. Atlant 12:07, (UTC) Reply It IS random! A picture of such a board with the probabilities marked on it would be helpful to understanding it.
#Galton board video series
Essentally, each peg in the bean machine/Galton board presents a left/right binary decision and the resulting bin that the the beans/balls eventually fall into is a result of a series of these left/right binary decisions.
Reply Give Binomial distribution a read and see if it answers your question. The article doesnt define why it just isnt random. Can anyone explain why it aproximates a bell curve or normal distribution?
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