Maths
8 breaks
Patterns, chance and the numbers hiding in everyday things.
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Why a treatment can win in every group and still lose overall: Simpson's paradox
Treatment B beats Treatment A overall, yet A wins for small stones and for large stones. That is Simpson's paradox, and it is real data from a kidney-stone…
Why a dropped stick can find π: Buffon's needle
Drop a stick on a floor of planks and count how often it lands across a seam. The count secretly contains π: for a needle as long as the plank width, the…
Why 23 people are enough for a shared birthday: counting pairs, not people
Put 23 people in a room and the chance that two share a birthday is already 51%. It feels far too low a number, because we picture one person matching our…
Why random bounces pile up into a bell curve: the Galton board
Every ball in a Galton board makes the same blind choice at each peg: left or right, a coin flip. Yet drop enough of them and the pile always grows into the…
Why switching doors wins twice as often: the Monty Hall problem
Three doors, one car. You pick one, the host opens a goat door, and offers a swap. Most people say it's 50/50. It isn't: switching wins twice as often as…
How dropping needles on a floor reveals the number π: Buffon's needle
Toss a match onto a plank floor and ask: does it touch a crack? Do it thousands of times and the fraction that do will quietly spell out π, though no circle is…
Why 23 people are enough for two to share a birthday
Put 23 people in a room and there's a better-than-even chance that two of them share a birthday. That sounds wrong, because 23 is tiny next to 365. The catch…
Why seven shuffles are enough to mix a deck of cards
A 52-card deck can be put in about 8 × 10^67 different orders, yet a few quick shuffles leave a lot of the old order behind. In 1992 Dave Bayer and Persi…