Browsing category probability

A reader asks: how long would you last in a casino?

Imagine you go to the casino with $100 in one-dollar chips and decide to play the roulette wheel. You've nothing better to do; you can stay there as long as you have chips left. How long can you expect to carry on playing? Let's pick on the 50-50 bets (such

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The Peculiar Maths of Birthdays

"How is it," asked my friend Jo, "that five of my friends are celebrating birthdays today?" This is, although it might not seem it, closely related to reading the minds of Alex Bellos's parents. By which I mean: randomness doesn't always look random. From here on in, I'm going to

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Bringing out the big gnus: runs of coins

* Thanks to Barney Maunder-Taylor for the problem In Alex's Adventures In Numberland, the author - Alex Bellos - makes a big production of getting one of his parents to pretend to toss a coin 20 times and the other to actually do it, then tell which one is which.

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Bayes’ Theorem and Minesweeper

I suppose I must have learned about Bayes' Theorem at sixth form. In those days, maths was Pure and Applied, so I could - and did - largely avoid statistics until midway through my PhD I was roundly mocked by my future boss for not knowing what 'significant' meant. I

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Lives of the Mathematical Ninja: Blaise Pascal

My current hero of mathematics - like Ramanujan - died before he was 40. Like Ramanujan, he'd already revolutionised maths by that point. Blaise Pascal (born in Clermont-Ferrand in central France in 1623) can reasonably claim to have invented probability theory, and the first calculator; he was also the first

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A Co-Proof of the Birthday Problem

“[In this context] Co- just means ‘opposite’ — so a co-mathematician is a machine for turning theorems into ffee.” — Miles () Matt Parker () laid down a challenge on Day 1 of the MathsJam conference: he said that proof by MathsJam was acceptable, because if it wasn’t true, you

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Would an infinite number of monkeys eventually write Shakespeare?

“If you had an infinite number of monkeys, there’d be no room for typewriters.” — Jason Arnopp Yes, an infinite number of monkeys would eventually — in fact, before very long at all — write Shakespeare. The problem, then, is finding which of the monkey-poo-smeared manuscripts is actually the whole

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Those medalling kids: knockout tournaments and who wins what?

(This piece is based on a paper I read recently... but I can't find a reference for it. If you know which paper I mean, please let me know and I'll update.) There's a reason tennis knockout draws are seeded. I'll get to why in a moment. But first, let's

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A question to which I don't know the answer: how to pick a parking space.

From time to time, I come across a problem that has me scratching my head. In a good way. I like brain-teasers. Sometimes I solve them, sometimes I don't. This is one that I haven't solved -- but I wanted to share the thought process that goes into modelling the

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Secrets of the Mathematical Ninja: Pascal’s Triangle

You've seen Pascal's triangle before: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 You get the number in each row by adding its two 'parents' - for instance, each 10 in the row that starts with 1

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