This paper deals with the study, from a probabilistic point of view, of logistic-type differential equations with uncertainties. We assume that the initial condition is a random variable and the diffusion coefficient is a stochastic process. The main objective is to obtain the first probability density function, f 1 (p, t), of the solution stochastic process, P(t, ω). To achieve this goal, first the diffusion coefficient is represented via a truncation of order N of the Karhunen-Loève expansion, and second, the Random Variable Transformation technique is applied. In this manner, approximations, say f N 1 (p, t), of f 1 (p, t) are constructed. Afterwards, we rigorously prove that f N 1 (p, t) −→ f 1 (p, t) as N → ∞ under mild conditions assumed on input data (initial condition and diffusion coefficient). Finally, three illustrative examples are shown.