A planar, unidirectional fibrous composite, which is an idealized random heterogeneous material consisting of stiff fibers of random strength embedded in parallel in a compliant matrix is discussed. It fractures in a brittle manner when the fibers engage in idealized, local load sharing. The matrix and fibers are assumed to be time independent. The brittle behavior, which is represented by a power distribution function, occurs irrespective of the disorder in fiber strengths. The result is established by calculating lower and upper bounding distributions for composite strength using the Chen-Stein theorem.