A Double Birthday Paradox in the Study of Coincidences

Coincidences are rare unexpected events that can fascinate, but their typical post hoc discovery and haphazard nature also have the potential to confuse and to confound correct scientific analysis. Mathematically, they can sometimes be modeled by birthday-problem collisions in datasets. In this paper, we take an expository approach to considering some of the issues involved in modeling of coincidences found from data searches and examine a double birthday problem that arises when multiple data sets are considered.