Motivated by important chemical engineering applications, we study probabilistic mechanisms of stochastic effects in a randomly forced model of the continuous stirred tank reactor. The bifurcation analysis of the deterministic model reveals the parameter zone of bistability with coexistence of the equilibrium and oscillatory regimes. It is shown that the boundary between basins of these regimes is moving as the bifurcation parameter changes. We study noise-induced transitions across this boundary leading to the stochastic generation of spiking oscillations and backward effect of the noise-induced suppression of large-amplitude spiking. In the study of these stochastic effects, we use statistics extracted from the direct numerical simulation, and an analytical approach using confidence ellipses method. An important probabilistic phenomenon of coherence resonance is revealed and discussed.