This paper explores the application of the Chen-Stein method to DNA sequence analysis. In particular, we are interested in the probability of detecting an unusual congruence between 2 sequences. We compare the results from theoretical prediction according to the Chein-Stein method, real data, and computer simulations. Statistical testing and confidence intervals are also provided to assess the accuracy of the theoretical results. Our results show that the Chen Stein method gives a decent estimate of the exact probability.