Simulation planche de galton1/30/2024 ![]() This is all very abstract but the concept can be made physical with a contraption called a Galton Board, named after Sir Francis Galton but also called a bean machine of quincunx. Another key characteristic of Pascal's Triangle is that the probabilities build up row by row into an approximation of the normal distribution. Probabilities always add up to 1, indicating certainty - if you start at the top and keep going, whatever path you take and wherever you end up, you are certain to get to one of the numbers in the last row. The total number of paths is 16 so the total probability isĥ-Row Pascal's Triangle Total Path Probabilities So for example in the 5-row triangle above the probability of taking a particular path is ![]() (We subtract 1 from the row count as there is no choice involved on the first row, there only being one number.) This is the graphic I used in the previous post to illustrate a five-row Pascal's Triangle.Ī key characteristic of Pascal's Triangle is that if you start at the top and than trace a path downwards, randomly choosing to go left or right, each number you land on tells you how many different paths there are to that number. ![]() I recently wrote a post on Pascal's Triangle and in this post I will write a program in Python to implement a Galton Board simulator, a Galton Board being an actual physical gadget following the Pascal Triangle's probabilistic characteristics. ![]()
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