The Easiest Problem Everyone Gets Wrong



Watch my newest video, "Surviving the Deadliest Two-Player Game": https://youtu.be/ACtsYN1TWLg Learn More: https://www.fullsail.edu/vsauce2 Thanks to Full Sail University for sponsoring this video and supporting Vsauce2. Special thanks to Internet Historian: https://www.youtube.com/channel/UCR1D15p_vdP3HkrH8wgjQRw Get Vsauce2’s Woven Math T-shirts/Hoodies: https://represent.com/store/vsauce2 We know how difficult the Monty Hall Problem is for so many people even after they’re shown all the math behind the best possible strategy. It’s basic probability, but it’s deceptive -- and it all started with the Bertrand’s 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 probabilités,” 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 Bertrand’s 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 -- Bertrand’s Box, Three Prisoners, and Monty Hall -- were paradoxes or simple 50/50 coin flips. It’s time to go back to the beginning… and show why there’s 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 Bertrand’s “Calcul des Probabilités”: 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, “Bertrand’s 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 *** Vsauce2: Twitter: https://twitter.com/VsauceTwo Facebook: https://www.facebook.com/VsauceTwo Talk Vsauce2 in the TCU Discord: https://discord.gg/tyh7AVm 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 Get Vsauce's favorite science and math toys delivered to your door! https://www.curiositybox.com/ #education #vsauce2 #learning
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The Easiest Problem Everyone Gets Wrong