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Network slicing allows Mobile Network Operators to split the physical infrastructure into isolated virtual networks (slices), managed by Service Providers to accommodate customized services. The Service Function Chains (SFCs) belonging to a slice are usually deployed on a best-effort premise: nothing guarantees that network infrastructure resources will be sufficient to support a varying number of users, each with uncertain requirements. Taking the perspective of a network Infrastructure Provider (InP), this paper proposes a resource provisioning approach for slices, robust to a partly unknown number of users with random usage of the slice resources. The provisioning scheme aims to maximize the total earnings of the InP, while providing a probabilistic guarantee that the amount of provisioned network resources will meet the slice requirements. Moreover, the proposed provisioning approach is performed so as to limit its impact on low-priority background services, which may co-exist with slices in the infrastructure network. A Mixed Integer Linear Programming formulation of the slice resource provisioning problem is proposed. Optimal joint and suboptimal sequential solutions are proposed. These solutions are compared to a provisioning scheme that does not account for best-effort services sharing the common infrastructure network.