In wireless sensor networks (WSNs), scheduling of the sensors is considered to be the most effective energy conservation mechanism. The random and unpredictable deployment of sensors in many WSNs in the open fields makes the sensor scheduling problem very challenging and randomized scheduling algorithms are thus used. The performance of these algorithms is usually analyzed using simulation techniques, which do not offer 100% accurate results. In this paper, we overcome this limitation by using higher-order-logic theorem proving to formally analyze the coverage-based random scheduling; a variant of the random scheduling algorithm designed for wireless sensor networks. Particularly, we aim at formalizing this coverage-based random scheduling within the probabilistic framework developed in the HOL theorem prover. We also formally reason about the expected values of coverage intensity, the upper bound on the total number of disjoint subsets, given expected coverage intensity, the lower bound on the total number of nodes and the average detection delay inside the network.