Pinching antennas, realized through position-adjustable radiating elements along dielectric waveguides, have emerged as a promising flexible-antenna technology thanks to their ability to dynamically reshape large-scale channel conditions. However, most existing studies focus on idealized LoS-dominated environments, overlooking the stochastic nature of realistic wireless propagation. This paper investigates a more practical multiuser pinching-antenna system under a composite probabilistic channel model that captures distance-dependent LoS blockage and NLoS scattering. To account for both efficiency and reliability aspects of communication, two complementary design metrics are considered: an average signal-to-noise ratio (SNR) metric characterizing long-term throughput and fairness, and an outage-constrained metric ensuring a prescribed reliability level. Based on these metrics, we formulate two optimization problems: the first maximizes the max-min average SNR across users, while the second maximizes a guaranteed SNR threshold under per-user outage constraints. Although both problems are inherently nonconvex, we exploit their underlying monotonic structures and develop low-complexity, bisection-based algorithms that achieve globally optimal solutions using only simple scalar evaluations. Extensive simulations validate the effectiveness of the proposed methods and demonstrate that pinching-antenna systems significantly outperform conventional fixed-antenna designs even under random LoS and NLoS channels.