The local search in tracking with a phased array radar can be characterized in terms of the events that can occur in the search and the probabilities of those events. In predicting the event probabilities, it is required to evaluate the expectation of a product of target detection probabilities for repeated beam-positioning in the local search. In this paper, we present a model of the local search and derive an expression for the expectation of the detection-probability product. An expression of angular measurement accuracy of target detection is also presented. Evaluation of the expressions requires numerical integration, which is computationally expensive. Approximations to the expressions are presented in analytic form, which are fairly accurate.