# Randomness, Well-posedness and Bertrand’s Paradox

Dr. Mihai Stoiciu

In a remarkable coincidence, in the same semester that Frank Morgan visited, we are fortunate enough to have another talk by a faculty member visiting from Williams College in Massachusetts.  This time it is Dr. Mihai Stoiciu.  He will be talking about the remarkable Bertrand’s Paradox on

Wednesday, March 31st at 5pm in PHSC 1105.

The short version of the Paradox is this:  If you ask a very simple question in probability (if you randomly choose a chord on the unit circle, what is the probability that it will be longer than $\sqrt{3}$?  That is, longer than the length of one of the sides of the inscribed equilateral triangle.), then there are multiple different and arguably correct answers.  How can one math question have multiple correct answers?  That’s the Paradox!  The answer is that the seemingly clear question is actually ill-posed — it all depends on what “randomly” means.   Dr. Stoiciu will talk about Bertrand’s Paradox and the can of worms it opens:

Title: Randomness, Well-posedness and Bertrand’s Paradox

Abstract: We will discuss Bertrand’s Paradox, a famous problem in probability. The question is the following: what is the probability that a random chord in a given circle is longer than the side of the equilateral triangle inscribed in the circle? Since the problem is not well-posed, we can find at least five “correct” answers to this question. We will present these different approaches and comment on the ideas of randomness and well-posedness.

As always, Free Pizza!

A few thousand random chords on the unit circle.

President Clinton also struggled with the issue of well-posedness: