This book delves into statistical challenges associated with the registration of individual particles, primarily focusing on discrete distributions such as Poisson and binomial distributions. It offers an in-depth examination of issues related to observing radioactive decay, counting statistics in various counting schemes, and the intricacies of coincidence circuits, as well as counters with "dead time." Aimed at experimental physicists working in the fields of nuclear and particle physics, this text provides essential insights and methodologies for navigating these complex statistical landscapes.