In the context of independent events, what does P(A given B) equal to?

In the context of independent events, the probability of event A given event B, denoted as P(A given B), is equal to the probability of event A, represented as P(A). This stems from the definition of independent events, which states that the occurrence of one event does not affect the occurrence of another. Therefore, when two events A and B are independent, the probability that A occurs is the same regardless of whether B occurs or not.

This means that knowing B has occurred gives no additional information about the likelihood of A occurring. Consequently, P(A given B) retains the original probability of A itself, which is P(A). This characteristic is fundamental in the study of probability and is commonly used in various applications.

The correct understanding of this principle is crucial for solving problems involving independent events, as it allows for a simplification of calculations surrounding conditional probabilities.