Deterministic vs Probabilistic Model

Deterministic  Model

A deterministic model is a mathematical model in which outcomes are precisely determined through known relationships among states and events, without room for random variation.

probabilistic model

A probability model is a mathematical representation of a random phenomenon, It is defined by it's sample, events within the sample space, and probabilities.

The models are also defined as statistical analysis tool that estimates, on the basis of past data, the probability of an event occurring. 

Unlike the deterministic model, the probabilistic model elements of randomness, This model is likely to produce different results even with the same initial conditions. There is always an element of chance or uncertainty involved which implies that there are possible alternate solutions.                                   

The probabilistic model includes both a deterministic component and a random error component.