Principles of Managerial Statistics and Data Science

5Introduction to Probability

5.1 Introduction

We need a measure that allows us to determine how feasible the occurrence of an event is. This will lead us closer to, among other things, being able to conduct statistical inference on population parameters. In this chapter, we will cover the topic of probability.

In practice, we encounter situations where it is convenient to use probabilities to make decisions. For example, if a company considers that a product price cut will result in an increase in sales of that product, the company can take a sample of days with sales and determine, through statistical inference, if the strategy works. Statistical inference requires probability. As another example, a shoe store knows by experience that 10% of the shoes from a certain brand are defective. The store wants to have a special sale of 100 pairs of shoes of that brand during a holiday. For the sale to succeed, management determines that they must sell 75 shoes with no defects. What is the probability that out of the 100 pair of shoes sold, 25 or more have defects? Furthermore, the store might be interested in finding if given that a customer buys a defective pair of shoes, what is the probability that the customer will return the shoes.

Why Probability?

Some general reasons why probability is necessary are as follows:

• Probability allows us to determine decisions that will maximize revenue and/or minimize costs.
• Probability allows risk control.
• Probability establishes business ...