The Online Math Olympiad is a contest for high school students with challenging problem. This 2016 test had an average score of 9 out of 30. This video is an adaption of problem 16 which is an interesting probability puzzle. At the end of day 0, six magical seeds are planted. On each day following, each seed has a chance to magically transform into an apple tree with a probability of 1/2. Once a seed transforms into an apple tree, it stays an apple tree and survives indefinitely. What is the expected number of days until all six seeds have become apple trees? Can you figure it out? Thanks to: Arbitrary Renaissance (null) for suggesting the problem and writing up a solution to fill in details from the official solution. My blog post for this video: https://wp.me/p6aMk-5oy Source Adapted from Fall 2016 OMO Problem 16: http://internetolympiad.org/archive/OMOFall16/OMOFall16Probs.pdf Online Math Olympaid homepage: http://internetolympiad.org/ Alex Knudson derivation of solution using Markov chains http://allmathsconsidered.com/2018/01/16/a-response-to-the-tricky-apple-tree-probability-problem/ If you like my videos, you can support me at Patreon: https://www.patreon.com/mindyourdecisions 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: https://mindyourdecisions.com/blog/ Twitter: https://twitter.com/preshtalwalkar Facebook: https://www.facebook.com/pages/Mind-Your-Decisions/168446714965 Google+: https://plus.google.com/108336608566588374147/posts Pinterest: https://www.pinterest.com/preshtalwalkar/ Tumblr: https://preshtalwalkar.tumblr.com/ Instagram: https://instagram.com/preshtalwalkar/ Patreon: https://www.patreon.com/mindyourdecisions Newsletter (sent about 2 times a year): http://eepurl.com/KvS0r 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 3.8/5 stars on 31 reviews) http://amzn.to/1uQvA20 "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 5/5 stars on 2 reviews) http://amzn.to/1o3FaAg "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. http://amzn.to/1GhUUSH "Math Puzzles Volume 2" is a sequel book with more great problems. (rated 5/5 stars on 3 reviews) http://amzn.to/1NKbyCs "Math Puzzles Volume 3" is the third in the series. (rated 3.8/5 stars on 4 reviews) http://amzn.to/1NKbGlp "40 Paradoxes in Logic, Probability, and Game Theory" contains thought-provoking and counter-intuitive results. (rated 4.3/5 stars on 12 reviews) http://amzn.to/1LOCI4U "The Best Mental Math Tricks" teaches how you can look like a math genius by solving problems in your head (rated 4.7/5 stars on 4 reviews) http://amzn.to/18maAdo "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 3 reviews) http://amzn.to/XRm7M4