Our topic is approximation to a solution \(\varphi (x)\) of the one-dimensional integral equation of the second kind \[ \varphi (x) = \int^b_a k(x',x) \varphi (x') dx' + \psi (x) \quad \text{or} \quad \varphi = K \varphi + \psi, \tag{1} \] where \(x \in [a,b] \subset \mathbb{R}\), the functions \(k\) and \(\psi\) are known, \(\psi \in L_\infty\), \(K \in [L_\infty \to L_\infty]\); moreover, \(|K_1 |< 1\), where \(K_1\) is the operator with kernel \(k_1 (x',x) = |k (x',x) |\). We study discrete-stochastic numerical procedures for global estimation of a solution to equation (1). We introduce a discrete mesh \(\{x_i\}\) in \([a,b]\), calculate the values \(\{\varphi (x_i)\}\) by the Monte Carlo method, and afterwards interpolate the function \(\varphi (x)\) by using the values at the nodes of the mesh.