Wireless sensor networks promise to guarantee accurate, fault tolerant and timely detection of events in large scale sensor fields. To achieve this the notion of k-coverage is widely employed in WSNs where significant redundancy is introduced in deployment as an event is expected to be sensed by at least k sensors in the neighborhood. As sensor density increases significantly with k, it is imperative to find the optimal k for the underlying event detection system. In this work, we consider the detection probability, fault tolerance and latency as the Quality of Service (QoS) metrics of an event detection system employing k-coverage and present a probabilistic model to guarantee given QoS support with the minimum degree of coverage taking into account the noise related measurement error, communication interference and sensor fault probability. This work eventually resolves the problem of over or under deployment of sensors, increases scalability and provides a well defined mechanism to tune the degree of coverage according to performance needs.