Probability Theory explores the mathematical framework for quantifying uncertainty and making informed decisions based on random events.
A random experiment is any process that can be repeated and has uncertain outcomes. Even if you do the same thing multiple times, you might get different results each time. That's the heart of probability!
An event is a set of outcomes from a random experiment. Events can be simple (like flipping a coin and getting heads) or compound (like rolling a dice and getting an even number).
The sample space is the set of all possible outcomes. For instance, when rolling a six-sided die, the sample space is \({1, 2, 3, 4, 5, 6}\).
Understanding random experiments and events is the foundation of probability. It helps you organize possible outcomes and figure out what you might expect to happen.
Tossing a coin (outcomes: heads or tails)
Drawing a card from a shuffled deck (outcomes: Ace, 2, ..., King of any suit)
Random experiments are processes with unpredictable outcomes, and events are sets of those outcomes.