What is the purpose of the Addition Law in probability?

The purpose of the Addition Law in probability is to compute the probability of the union of two events. This law provides a systematic way to find the likelihood that at least one of two events occurs. When calculating the probability of the union of events ( A ) and ( B ), the formula is expressed as:

[ P(A \cup B) = P(A) + P(B) - P(A \cap B) ]

This equation highlights two important aspects: it adds the probabilities of the individual events and then subtracts the probability of their intersection to avoid double counting the outcomes where both events occur.

Understanding this law is crucial for various applications in probability, especially in cases where events overlap. It allows for a comprehensive approach to assess overall probabilities in compound scenarios, reflecting real-world situations where multiple events may occur simultaneously.