Category Archives: probability

Have a piece of PIE

Posted on July 21, 2019 by Brent

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 →

Posted in pattern, probability | Tagged , | 6 Comments

Probabilistic PIE

Posted on July 17, 2019 by Brent

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 →

Posted in pattern, probability, solutions | Tagged , | 7 Comments

A probabilty puzzle

Posted on July 15, 2019 by Brent

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 →

Posted in challenges, probability | Tagged , | 9 Comments

Network reliability

Posted on February 22, 2016 by Brent

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 one-directional wires between them. Each … Continue reading →

Posted in links, probability | Tagged , , , | 2 Comments

The birthday candle problem: solution

Posted on August 25, 2015 by Brent

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 , , , | 5 Comments

The birthday candle problem

Posted on August 7, 2015 by Brent

After a 1.5-month 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 , , , | 5 Comments

The mathematics of human knots

Posted on November 19, 2010 by Brent

Have you ever played “human knot”? It seems to be a common icebreaker/team-building 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 , , , , , | 9 Comments

Change probabilities

Posted on June 9, 2008 by Brent

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

Posted on July 28, 2006 by Brent

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