A quantum of transmitter may be released upon the arrival of a nerve impulse if the influx of calcium ions through a nearby voltage-dependent calcium channel is sufficient to activate the vesicle-associated calcium sensor protein that triggers exocytosis. A synaptic vesicle, together with its calcium sensor protein, is often found complexed with the calcium channel in active zones to form what will be called a "synaptosecretosome." In the present work, a stochastic analysis is given of the conditions under which a quantum is released from the synaptosecretosome by a nerve impulse. The theoretical treatment considers the rise of calcium at the synaptosecretosome after the stochastic opening of a calcium channel at some time during the impulse, followed by the stochastic binding of calcium to the vesicle-associated protein and the probability of this leading to exocytosis. This allows determination of the probabilities that an impulse will release 0, 1, 2,... quanta from an active zone, whether this is in a varicosity, a bouton, or a motor endplate. A number of experimental observations of the release of transmitter at the active zones of sympathetic varicosities and boutons as well as somatic motor endplates are described by this analysis. These include the likelihood of the secretion of only one quantum at an active zone of endplates and of more than one quantum at an active zone of a sympathetic varicosity. The fourth-power relationship between the probability of transmitter release at the active zones of sympathetic varicosities and motor endplates and the external calcium concentration is also explained by this approach. So, too, is the fact that the time course of the increased rate of quantal secretion from a somatic active zone after an impulse is invariant with changes in the amount of calcium that enters through its calcium channel, whether due to changes consequent on the actions of autoreceptor agents such as adenosine or to facilitation. The increased probability of quantal release that occurs during F1 facilitation at the active zones of motor endplates and sympathetic boutons is predicted by the residual binding of calcium to a high-affinity site on the vesicle-associated protein. The concept of the stochastic operation of a synaptosecretosome can accommodate most phenomena involving the release of transmitter quanta at these synapses.