An Insanely Hard Probability Paradox

You throw a dice until you get 6. What is the expected number of throws (including the throw giving 6) conditioned on the event that all throws gave even numbers? This is Elchanan Mossel’s Amazing Dice Paradox, and it's one of the best mathematical veridical paradoxes I have seen. We discuss the problem and the probability underlying the right and wrong answers. #maths #mathpuzzle #mathematics More math chats: https://www.youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join sources: https://gilkalai.wordpress.com/2017/09/07/tyi-30-expected-number-of-dice-throws/#comment-35615 https://www.yichijin.com/files/elchanan.pdf https://medium.com/p/6cf74ebb3847 https://math.stackexchange.com/questions/2779681/expected-number-of-die-rolls-to-get-6-given-that-all-rolls-are-even ★DONATE★ ◆ Support Wrath of Math on Patreon: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 1:34 Some Trials 2:49 Poll Results 5:14 Intuitive Explanation 12:36 The Flaw in the Argument 15:07 Expected Value Calculation 21:58 Conclusion