Probability Theory explores the mathematical framework for quantifying uncertainty and making informed decisions based on random events.
Probability isn't always just about counting! There are three main approaches:
This method assumes all outcomes are equally likely. It's great for games and puzzles where everything is fair.
Here, you estimate probability based on actual experiments or past data. More trials mean more reliable results.
Sometimes, probability is based on personal belief or best guess, like a weather forecast or a sports prediction.
Depending on the situation, one type might be more useful or practical than another.
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.
Classical, empirical, and subjective probabilities help us estimate likelihoods in different ways.