MathomalyA field guide to patterns, proofs and open questions

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The Mathomaly series

Short explainers about patterns that look certain and are not. Each episode ends on the explorations you can try yourself.

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No. 039:13

Why does chance fool us?

You bet on a pattern of three flips, I pick mine after you, and with one fair coin I win at least two games in three: whatever you pick, there is a pattern that beats it. A positive result from a 99% accurate test for a rare illness is right only about 1 time in 11, and a kidney-stone treatment can do better for small stones and for large ones yet worse overall: each time, we counted the wrong thing.

Chapters

  1. 0:00I pick secondTry it →
  2. 1:24One fair coinTry it →
  3. 3:50The 99% test
  4. 6:10Kidney stones
  5. 8:04Counting the wrong thing
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3 episodes