A Revolving Door Birthday Problem

The traditional "birthday problem" considers the probability of two or more people in a group of N sharing a birthday. This paper generalizes the problem to consider the conditional probability of transitioning from a given distribution of birthdays to another when one person leaves the group of N and another enters as if through a revolving door. Markov chains are used to model the transitions. The problem is an interesting extension of a classic probability problem and is a vehicle for illustrating Markov chains and numerical methods for handling large sparse matrices.

Mathematical Reviews Classification: 60C05, 60J20