P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.4 + 0.3 - (0.4 \cdot 0.3) = 0.7 - 0.12 = 0.58

Tue, 05 May 2026 19:22:36 +0000

Understanding the Probability Formula: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) — A Complete Guide to Combining Events In probability theory, one of the most fundamental concepts is calculating the likelihood that at least one of multiple events will occur. This is expressed by the key formula: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) This equation helps us find the probability that either event A or event B (or both) happens, avoiding double-counting the overlap between the two events. While it applies broadly to any two events, it becomes especially useful in complex probability problems involving conditional outcomes, overlapping data, or real-world decision-making.