Estimation of the number of stem cells involved in repopulationof the bone marrow following marrow transplantation usuallyrelies on methods of cell biology. The amount of stem cellsinvolved in this process may be a determinant of a numberof potential complications of the disease.Statistical methods relying upon some simple assumptionsconcerning cell dynamics can also be used. The problem thenbecomes one which can be framed in a context of binomialsampling. However, unlike the more classic problem where wecondition upon some value n and make inference on a populationparameter p based on the observed number of successes, hereinference is focussed upon n. We are unable to observe thenumber of successes directly. Bayesian methods are also possible.