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Category Archives: probability
Have a piece of PIE
Commenter Stuart LoPresti gave a very nice analysis answering the questions at the end of my last post. And indeed, the punchline is that the answers are very similar to the answers to the post before that. PIE If we … Continue reading
Probabilistic PIE
Commenters Sylvain B., xpil, and Christian Luca all gave correct answers to the challenge from my previous post. If the probability that someone likes X is , then the probability they don’t like X is . Therefore the probability that … Continue reading
A probabilty puzzle
Suppose that we have surveyed a certain population of people, and have determined the following probabilities: The probability that a person likes anchovies is . The probability that a person likes to read books is . The probability that a … Continue reading
Network reliability
Over on my other blog I’ve started writing about an interesting but apparently nontrivial problem, which some readers of this blog may find interesting as well. Suppose you have a network of computers with some onedirectional wires between them. Each … Continue reading
The birthday candle problem: solution
Recall the birthday candle problem I wrote about in a previous post: A birthday cake has lit candles. At each step you pick a number uniformly at random and blow out candles. If any candles remain lit, the process repeats … Continue reading
Posted in combinatorics, probability, solutions
Tagged birthday, candles, expectation, problem
5 Comments
The birthday candle problem
After a 1.5month epic journey1, I am finally settling into my new position at Hendrix College. Here’s a fun problem I just heard from my new colleage Mark Goadrich: A birthday cake has lit candles. At each step you pick … Continue reading
Posted in challenges, combinatorics, probability
Tagged birthday, candles, expectation, problem
5 Comments
The mathematics of human knots
Have you ever played “human knot”? It seems to be a common icebreaker/teambuilding sort of exercise (just do a Google search for “human knot” and you’ll find quite a few pages discussing it). Everyone stands in a circle, then reaches … Continue reading
Posted in games, people, probability
Tagged games, human, icebreaker, knot, team, teambuilding
9 Comments
Change probabilities
Hello, dear reader! If you are a new reader, welcome! (I know there is at least one of you—thanks to commenter sg211 for prompting me to post again. =) I must apologize for dropping the ball on writing up the … Continue reading
Posted in challenges, counting, probability
17 Comments
Challenge #7
This delightful problem is courtesy of Diana Davis (don’t follow the link unless you want to see the solution, though!), although I did take the liberty of formulating it slightly differently. =) One bright and sunny day, you’re walking down … Continue reading
Posted in challenges, geometry, probability
7 Comments