The knapsack problem is a problem in combinatorial optimization that seeks to maximize the objective function $\sum_{i = 1}^{n} v_ix_i$ subject to the constraints $\sum_{i = 1}^{n} w_ix_i \leq W$ and $x_i \in \{0, 1\}$, where $\mathbf{x}, \mathbf{v} \in \mathbb{R}^{n}$ and $W$ are provided. We consider the stochastic variant of this problem in which $\mathbf{v}$ remains deterministic, but $\mathbf{x}$is an $n$-dimensional vector drawn uniformly at random from $[0, 1]^{n}$. We establish a sufficient condition under which the summation-bound condition is almost surely satisfied. Furthermore, we discuss the implications of this result on the deterministic problem.