March 2026
Intermediate
512 pages
14h 19m
English
Content preview from Mathematics in Cybersecurity
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11Basic Concepts of Probability
Imagine you are tossing a fair coin. What is the probability that it lands heads up? You might think the answer is obvious—50%. But probability is more than just guessing outcomes. It's a way of understanding the likelihood of various outcomes for events that involve uncertainty (the existence of several different results), and plays a crucial role in decision-making, statistics, science, and everyday life. Whether you are trying to predict the weather, assessing the odds of winning a game, or calculating risks in business, probability is the language of uncertainty.
In a sense, probability is a predictive science. By this, we mean we are looking ahead in time and asking, “How likely is a particular outcome to occur?”
In this chapter, we will explore the foundational concepts of probability, starting with simple experiments like coin flips and dice rolls. We will learn to calculate the likelihood of events happening, the difference between independent and dependent events, and how probability helps us make sense of the world in situations where randomness is involved.
By the end of this chapter, you'll be equipped with the basic tools to begin thinking probabilistically—an essential skill for anyone working in fields such as finance, engineering, computer science, or even genetics.
11.1 Experiments, Outcomes, Sample Spaces, and Events
Probability is a mathematical tool used to study randomness. It deals with the chance (or likelihood) of one ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.