Discrete Probability: Intro

Probability Theory is the mathematical study of uncertainty and randomness, and it allows us to model and predict the likelihood of various outcomes in uncertain scenarios. Discrete probability focuses specifically on systems where the set of possible outcomes is countable or finite, such as rolling dice, flipping coins, or drawing cards. In such discrete contexts, we can list all possible outcomes individually.

This field is especially relevant in computer science, where algorithms often rely on random inputs, simulations, and probabilistic reasoning to function efficiently. Applications of discrete probability in computer science include randomized algorithms, data structures like hash tables, network protocols, artificial intelligence, and machine learning.

Understanding how to compute and manipulate probabilities is crucial for making informed decisions under uncertainty, which is common in automated systems. Moreover, many encryption and cybersecurity techniques rely on probabilistic principles to ensure unpredictability and security of data.

This topic will help us build intuition and formal tools for analyzing randomness in computing contexts.