We present a dynamic programming based solution to a probabilistic reach-avoid problem for a controlled discrete time stochastic hybrid system We address two distinct interpretations of the reach-avoid problem via stochastic optimal control In the first case a sum-multiplicative cost function is introduced along with a corresponding dynamic recursion which quantifies the probability of hitting a target set at some point during a finite time horizon while avoiding an unsafe set during each time step preceding the target hitting time In the second case we introduce a multiplicative cost function and a dynamic recursion which quantifies the probability of hitting a target set at the terminal time while avoiding an unsafe set during the preceding time steps In each case optimal reach while avoid control policies are derived as the solution to an optimal control problem via dynamic programming Computational examples motivated by two practical problems in the management of fisheries and finance are provided (C) 2010 Elsevier Ltd All rights reserved