This paper proposes a virtual network function (VNF) placement model considering both availability and probabilistic protection for the service delay to minimize the service deployment cost. Both availability and service delay are key requirements of services; a service provider handles the VNF placement problem with the goal of minimizing the service deployment cost while meeting these and other requirements. The previousworks do not consider the delay of each route which the service can take when considering both availability and delay in the VNF placement problem; only the maximum delay was considered. We introduce probabilistic protection for service delay to minimize the service deployment cost with availability. The proposed model considers that the probability that the service delay, which consists of networking delay between hosts and processing delay in each VNF, exceeds its threshold is constrained within a given value; it also considers that the availability is constrained within a given value. We develop a two-stage heuristic algorithm to solve the VNF placement problem; it decides primary VNF placement by solving mixed-integer second-order cone programming in the first stage and backup VNF placement in the second stage. We observe that the proposed model reduces the service deployment cost compared to a baseline that considers the maximum delay by up to 12%, and that it obtains a feasible solution while the baseline does not in some examined situations.