A new equation, called the neutron multiplicity equation (NME), has been derived starting from basic physics principles. Neutron multiplicity υ is defined as the integral number of neutrons leaking from a neutron multiplying system for a source neutron introduced into it. Probability distribution of neutron multiplicities (PDNMs) gives the probability of leakage of neutrons as a function of their multiplicity v. The PDNM is directly measurable through statistical correlation techniques. In a specific application, the NME has been solved for PDNM as a function of v for 9Be spheres of varying radii and driven by a centrally located 14-MeV deuterium-tritium neutron source. The potential of NME for sensitivity analysis is demonstrated through a particular modification of secondary neutron transfer cross sections of 9Be. It turns out that PDNM is very sensitive, even as the “average” neutron leakage is practically insensitive to it.