Probability Theory

Probability Theory explores the mathematical framework for quantifying uncertainty and making informed decisions based on random events.

Basic Concepts

Types of Probability

Different Ways to Think About Probability

Probability isn't always just about counting! There are three main approaches:

Classical Probability

This method assumes all outcomes are equally likely. It's great for games and puzzles where everything is fair.

Empirical (Experimental) Probability

Here, you estimate probability based on actual experiments or past data. More trials mean more reliable results.

Subjective Probability

Sometimes, probability is based on personal belief or best guess, like a weather forecast or a sports prediction.

Why Use Different Types?

Depending on the situation, one type might be more useful or practical than another.

Examples

  • Classical: The chance of drawing a red marble from a bag with 5 red and 5 blue marbles is 5/10.

  • Empirical: After flipping a coin 100 times, you observe 54 heads, so the empirical probability of heads is 54/100.

In a Nutshell

Classical, empirical, and subjective probabilities help us estimate likelihoods in different ways.