When C3H/10T1/2 cells are treated with a given concentration of a chemical carcinogen, the transformation frequency can vary over 4 orders of magnitude, depending primarily upon the number of cells plated. To explain this phenomenon, the authors have developed a probabilistic theory of the formation of transformed foci in this system. The authors define P1 as the probability that a cell will be activated by carcinogen treatment, P2 as the probability per cell generation that an activated cell will be transformed, and P3 as the probability per cell generation that an activated cell will be deactivated. The equation we have derived: log (F/N) = log (2p1p2(1-p3)/2(1-p3)-1) + n log(1-p3) describes focus formation; F is mean number of foci per dish after carcinogen treatment, N is number of cells in a dish at confluence, and n is number of cell generations to confluence. This equation has been verified experimentally; p3=0.24 and p1p2=3.8X10 to the minus 6 power at a single concentration of 3-methylcholanthrene. This relationship explains previously inexplicable effects of cell density on transformation frequency.