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The Easiest Problem Everyone Gets Wrong

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Channel: Vsauce2
Categories: Brain Teasers   |   Statistics & Probability   |   Math  
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Watch my newest video, "Could a Toothpaste Sandwich Brush Your Teeth?": https://youtu.be/OdeiWhETqQY

We know how difficult the Monty Hall Problem is for so many people even after theyre shown all the math behind the best possible strategy. Its basic probability, but its deceptive -- and it all started with the Bertrands Box Paradox.

In this video, I go back to the origins of a probability problem that continues to plague humanity. And it all started in 1889 when French mathematician Joseph Bertrand published his Calcul des probabilits, which included a simple scenario involving gold and silver coins.

70 years later, recreational math columnist Martin Gardner unveiled The Three Prisoners Problem involving the pardoning of one of three prisoners scheduled to be executed. The mathematical concept was the same as Bertrands Box, but The Three Prisoners continued to be a probability paradox that haunted everyone from the readers of Scientific American to professional mathematicians.

But the Monty Hall Problem is really what made this mathematical illusion explode. By the 1990s, there was an all-out argument about whether all of these problems -- Bertrands Box, Three Prisoners, and Monty Hall -- were paradoxes or simple 50/50 coin flips. Its time to go back to the beginning and show why theres something even more important than solving this math problem.

*** SOURCES ***

Krauss and Wang, The Psychology of the Monty Hall Problem: Discovering Psychological Mechanisms for Solving a Tenacious Brain Teaser: https://www.researchgate.net/publication/10839512_The_Psychology_of_the_Monty_Hall_Problem_Discovering_Psychological_Mechanisms_for_Solving_a_Tenacious_Brain_Teaser

Why Humans Fail in Solving the Monty Hall Dilemma: A Systematic Review: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6194549/

Joseph Bertrands Calcul des Probabilits: https://archive.org/download/calculdesprobab00bertgoog/calculdesprobab00bertgoog.pdf

Dan MacKinnon (mathrecreation), Monty Hall and The Three Prisoners: http://www.mathrecreation.com/2009/03/monty-hall-and-three-prisoners.html

Dan Jacob Wallace, Bertrands Box Paradox (With and Without Bayes Theorem): https://www.untrammeledmind.com/2018/11/bertrands-box-paradox/

Eugene P. Northrop, Riddles in Mathematics: https://archive.org/details/RiddlesInMathematics/page/n167/mode/2up

*** LINKS ***

Special thanks to Internet Historian: https://www.youtube.com/channel/UCR1D15p_vdP3HkrH8wgjQRw

Vsauce2:
Twitter: https://twitter.com/VsauceTwo
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Hosted and Produced by Kevin Lieber
Instagram: http://instagram.com/kevlieber
Twitter: https://twitter.com/kevinlieber
Podcast: https://www.youtube.com/thecreateunknown

Research And Writing by Matthew Tabor
https://twitter.com/TaborTCU

Editing by John Swan
https://www.youtube.com/channel/UCJuSltoYKrAUKnbYO5EMZ2A

Huge Thanks To Paula Lieber
https://www.etsy.com/shop/Craftality

Select Music By Jake Chudnow: http://www.youtube.com/user/JakeChudnow

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