One practical goal of sensor deployment in the design of distributed sensor systems is to achieve an optimal monitoring and surveillance of a target region. The optimality of a sensor deployment scheme is a tradeoff between implementation cost and coverage quality levels. In this paper, we consider a probabilistic sensing model that provides different sensing capabilities in terms of coverage range and detection quality with different costs. A sensor deployment problem for a planar grid region is formulated as a combinatorial optimization problem with the objective of maximizing the overall detection probability within a given deployment cost. This problem is shown to be NP-complete and an approximate solution is proposed based on a two-dimensional genetic algorithm. The solution is obtained by the specific choices of genetic encoding, fitness function, and genetic operators such as crossover, mutation, translocation for this problem. Simulation results of various problem sizes are presented to show the benefits of this method as well as its comparative performance with a greedy sensor placement method.