Bayes' Theorem is a fundamental concept in probability and statistics. It allows us to update our initial beliefs about an event based on new evidence. Here's a step-by-step breakdown of the theorem, its components, and a couple of examples to solidify understanding.
- Independent Events: If events A and B are independent (they don't influence each other), then the probability that both occur is simply the product of their individual probabilities.
[ P(A \text{ and } B) = P(A) \times P(B)