Probability Theory explores the mathematical framework for quantifying uncertainty and making informed decisions based on random events.
Two events are independent if the occurrence of one does not affect the probability of the other. If they do affect each other, they're dependent.
For independent events \(A\) and \(B\):
\[ P(A \cap B) = P(A) \times P(B) \]
Knowing if events are independent helps you multiply probabilities correctly and avoid mistakes, especially in games or statistics.
Understanding independence is crucial in fields like genetics, risk analysis, and computer science.
Flipping two different coins: the result of one flip does not change the outcome of the other.
Drawing two cards from a deck without replacing the first card: the outcome of the first draw affects the second.
Events are independent if one doesn't affect the other; otherwise, they're dependent.