Lesson 10

Finally, let \(U=B_{1} \sqcup B_{2} \sqcup \dotsb \sqcup B_{n}\) — a partition of the sample space into events of positive probability. Then \[\Pr[A]= \sum_{i=1}^{n}\Pr[A \cap B_{i}]=\sum_{i=1}^{n}\Pr[A \mid B_{i}] \cdot \Pr[B_{i}] \ .\] This is the law of total probability.