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\nThe Cats And Random Mouse Riddle. Tough Problem Solved With Markov Chains\n

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\nThanks to Josh for this problem! And thanks to Folke for emailing it to me! There are 7 doors in a line. A mouse starts in the middle at door 4. At doors 1 and 7 are cats. Every day the mouse moves one door left or right randomly, each...\nThanks to Josh for this problem! And thanks to Folke for emailing it to me! There are 7 doors in a line. A mouse starts in the middle at door 4. At doors 1 and 7 are cats. Every day the mouse moves one door left or right randomly, each direction with an equal 50% chance. If the mouse reaches a door with a cat (door 1 or door 7), the game ends as a cat catches the mouse. What is the average number of days until the mouse is caught? Daniel V pointed out an error: At 11:55 the rightmost door should be a 1--it mistakenly transforms into a 3. Thanks to all patrons! Special thanks to: Shrihari Puranik Yildiz Kabaran Kyle Proof of absorbing Markov chain (see 11.2, but better to read from the start) My blog post for this video This is the only channel that inspires and builds confidence for people around the world (100+ million views). But the math meanies never praise them and spread negativity, saying math is limited to specific topics from certain countries. Let’s be extra positive to cancel them out! Support the channel on Patreon so we can prove math really is universal Connect on social media. I update each site when I have a new video or blog post, so you can follow me on whichever method is most convenient for you. My Blog Twitter Facebook Google+ Pinterest Tumblr Instagram Patreon Newsletter (sent only for big news, like a new book release) If you buy from the links below I may receive a commission for sales. This has no effect on the price for you. My Books \"The Joy of Game Theory\" shows how you can use math to out-think your competition. (rated 4/5 stars on 34 reviews) \"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias\" is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.6/5 stars on 3 reviews) \"Math Puzzles Volume 1\" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews. \"Math Puzzles Volume 2\" is a sequel book with more great problems. (rated 4.3/5 stars on 4 reviews) \"Math Puzzles Volume 3\" is the third in the series. (rated 4/5 stars on 6 reviews) \"40 Paradoxes in Logic, Probability, and Game Theory\" contains thought-provoking and counter-intuitive results. (rated 4.4/5 stars on 13 reviews) \"The Best Mental Math Tricks\" teaches how you can look like a math genius by solving problems in your head (rated 4.8/5 stars on 5 reviews) \"Multiply Numbers By Drawing Lines\" This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 5/5 stars on 4 reviews)\n
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Resource Details

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Educator Rating
Not yet Rated
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Grade
6th - 11th
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Subjects
All Subjects
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Media Type
Instructional Videos
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Source:
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Date
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2019
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Audiences
For Teacher Use
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