P = 12

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A simple diagram of a one-dimensional random walk. A red dot represents a particle at the center position. Arrows show the particle can move left or right with equal probability (P = 1/2).

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Sophie Maclean is a mathematician and maths communicator, currently studying for a PhD in Analytic Number Theory at Kings College London. She has previously worked as a Quantitative Trader and a Software Engineer, and now gives mathematics talks all over the UK (and Europe!). She is also a member of the team behind Chalkdust Magazine. You can follow her on Twitter at @sophietmacmaths

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