Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 3

Elements of Probability

The focus of this chapter is basic concepts of probability. The topics covered are:

• Random experiments and sample spaces
• Representations of sample spaces and events using Venn diagrams
• Basic concepts of probability
• Additive and multiplicative rules of probability
• Techniques of counting sample points: permutations, combinations, and tree diagrams
• Conditional probability and Bayes’ theorem
• Introducing random variables

Learning Outcomes

After studying this chapter, the reader will be able to

• Handle basic questions about probability using the definitions and appropriate counting techniques.
• Understand various characteristics and rules of probability.
• Determine probability of events and identify them as independent or dependent.
• Calculate conditional probabilities and apply Bayes’ theorem for appropriate experiments.
• Understand the concept of random variable defined over a sample space.

Introduction

In day-to-day activities and decisions we often confront two scenarios: one in which we are certain about the outcome of our action and the other in which we are uncertain or at a loss. For example, in making a decision about outcomes, an engineer knows that a computer motherboard requires four RAM chips and plans to manufacture 100 motherboards. The engineer is certain that he will need 400 RAM chips. On the other hand, the manufacturing process of the RAM chips produces both non-defective and defective chips. In this case the engineer focuses on how ...