A model is presented for the flash response of bioluminescent dinoflagellates stimulated by fluid shear. The model is based on the idea that the response of an individual cell to stimulation is inherently probabilistic, and can be modeled as a Poisson process over short time scales. A new cell parameter, the cell anxiety, is introduced to parameterize the probability of flashing. The statistical model is incorporated into a description of fully developed fluid flow in pipes and a cylindrical Couette chamber, and found to compare favorably with previously published data from experiments.