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The coin flip conundrum - Po-Shen Loh

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When you flip a coin to make a decision, there's an equal chance of getting heads and tails. What if you flipped two coins repeatedly, so that one option would win as soon as two heads showed up in a row on that coin, and one option would win as soon as heads was immediately followed by tails on the other? Would each option still have an equal chance? Po-Shen Loh describes the counterintuitive math behind this question.

If you flip a coin 1001 times, the expected number of consecutive heads-heads occurrences is exactly 250, which is also exactly the same as the expected number of consecutive heads-tails pairs. Why, then, is the expected time until the first consecutive heads-heads occurrence longer?

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Meet The Creators

  • Educator Po-Shen Loh
  • Director Mimi Chiu
  • Script Editor Eleanor Nelsen
  • Producer Aaron Augenblick
  • Animator Mimi Chiu
  • Collaborator Andrea Janov , Zach Nelkin, Mark Paulson
  • Associate Producer Elizabeth Cox, Jessica Ruby
  • Content Producer Gerta Xhelo
  • Editorial Producer Alex Rosenthal
  • Narrator Addison Anderson
  • Fact-Checker Brian Gutierrez

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