At very low radiation dose rates, the effects of energy depositions in cells by ionizing radiation is best understood stochastically, as ionizing particles deposit energy along tracks separated by distances often much larger than the size of cells. We present a thorough analysis of the stochastic impact of the natural radiative background on cells, focusing our attention on E. coli grown as part of a long term evolution experiment in both underground and surface laboratories. The chance per day that a particle track interacts with a cell in the surface laboratory was found to be 6 × 10-5 day-1, 100 times less than the expected daily mutation rate for E. coli under our experimental conditions. In order for the chance cells are hit to approach the mutation rate, a gamma background dose rate of 20 μGy hr-1 is predicted to be required.