**1. Introduction**

Many critical business challenges involve decision-making under uncertainty. Some examples of decision-making under uncertainty in the business world include decision to introduce a new product, capital budgeting decisions, strategic decisions to increase net profit and decisions to grant loans by a financial institution. Accounting for these sources of uncertainty and balancing the objectives of the business can be very challenging. This chapter discusses probabilistic modelling using Monte Carlo methods in modelling of decision problems. The focus is on using Monte Carlo simulation to provide a quantitative assessment of uncertainties and critical risk drivers in business decisions. Given adequate data and reasonable assumptions, probabilistic modelling techniques, such as Monte Carlo analysis can be viable statistical tools for analyzing uncertainty in business decisions. To make the most out of probabilistic modelling using Monte Carlo methods, executives must combine all available insights about the relevant uncertainties and their impact on their decisions.

Literature uses the terms probabilistic and stochastic modelling interchangeably. It is essential to provide a brief definition of these terms. Probabilistic modelling is a statistical technique used to consider the impact of random events or uncertainty in predicting the potential occurrence of future outcomes [1, 2]. Probabilistic models

incorporate probability distributions into the model of an event or phenomenon. These models are hinged on the premise that we rarely know everything about a situation. Therefore, there is always an element of randomness or uncertainties to consider. On the other hand, stochastic modelling forecasts the probability of various outcomes under different conditions using random variables [3]. The word stochastic comes from the Greek word *stokhazesthai*, meaning to aim or guess. Essentially, a stochastic model estimates probability distributions of potential outcomes by accounting for random variation in the input variables. Some examples of stochastic models include Monte Carlo simulation and Markov chain models amongst others [3]. These models use probability distributions to account for uncertainties in the input variables. In a strict sense, stochastic modelling is an area of probability and statistics used in decision-making under uncertainties. Like probability modelling, stochastic modelling presents data and predicts outcomes that account for certain levels of unpredictability or randomness. In this chapter, we use probabilistic and stochastic modelling interchangeably because both models are based on probability or the fact that randomness plays a role in predicting future events. The stochastic approach we will use is the Monte Carlo simulation method.

Using an example based on hypothetical data, we illustrate decision problems where uncertainties make probabilistic/stochastic modelling useful to obtain decision insights and explore alternative choices. We will explore how to propagate uncertainty in input decision variables to get a probability distribution of the output(s) of interest. The rest of the chapter is structured as follows. Section 2 discusses probability distributions and the distributions used in the example (Normal, Lognormal, Bernoulli, and Triangular distributions). Section 3 explores how to deal with uncertainty using a probabilistic/stochastic model. Section 4 provides an application of Monte Carlo methods in making business decisions, while Section 5 is the conclusion.
