Conditional Probability

Conditional probability answers a simple question: how does knowing one event has happened change the chance of another? For example, if you know it rained today, the probability that the ground is wet is no longer the same as it was before you had that information. This idea — updating probabilities in light of new evidence — is the heart of conditional probability, written as $P(A|B)$ and read as "the probability of $A$ given $B$." It is not just a formula; it is how …