Introduction to Probability

Probability theory is the branch of mathematics that deals with uncertainty and the likelihood of different outcomes. Understanding probability is essential for data science, as it allows you to model randomness, make predictions, and quantify risk in real-world situations.

To start, you need to know some key definitions:

• Experiment: an experiment is any process or action with uncertain results that can be repeated.
  Example: tossing a coin, rolling a die, or drawing a card from a deck;
• Outcome: an outcome is a single possible result of an experiment.
  Example: getting $"\text{heads}"$ when tossing a coin, or rolling a $4$ on a die;
• Sample Space: the sample space is the set of all possible outcomes of an experiment.
  Example: for a coin toss, the sample space is $\{"\text{heads}", "\text{tails}"\}$. For rolling a standard die, the sample space is $\{1, 2, 3, 4, 5, 6\}$;
• Event: an event is any collection of outcomes from the sample space, often described by a specific condition.
  Example: Rolling an even number on a die is an event that includes the outcomes $\{2, 4, 6\}$.

These concepts form the building blocks for all probability calculations and reasoning.