Realization of an extremely rare event can lead to enormous consequences. Examples include earthquakes, meteor impacts or genetic mutations. Understanding of the underlying statistical properties of such events is of great importance. However, investigation of these problems is very hard. The events are very rare and therefore it is extremely difficult to collect sufficient statistical data. We will address the problem of errors in information transmission through optical fibers as an example of such a rare event. Current limits for acceptable error rates in optical information systems allow approximately one error per billion or thousand billion bits. These errors result from the combination of noise and structural disorder in the system. Evaluation of the statistics of such errors is an important practical problem. However, straightforward Monte-Carlo type simulations for such rare events are not practical. On the other hand, designing systems by trial and error where each system is built is prohibitively expensive. In the framework of a mathematical model which we developed, we considered optical pulse (bit-carriers) dynamics in the presence of temporal system noise and structural disorder. Using the operator integral approach invented by Feynman, we found an analytical formula characterizing the statistics of errors as a function of system parameters and noise/disorder characteristics. These theoretical findings were verified against experimental data obtained at the Optical Sciences Center of the University of Arizona.