 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2003/calculus-probability-linear-algebra-discrete-mathematics-logic-and-proof-and-models-of-computation/5/a/ii/solution

B_{1}, B_{2}, \dots

form a finite or countable partition of a sample space into pairwise disjoint events with positive probabilities, then for any event

A

P (A) = j \sum P (A ∣ B_{j}) P (B_{j}) .

Indeed,

A

A \cap B_{j}

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