 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/discrete-mathematics-continuous-mathematics-and-probability/8/a/ii/solution

P (A) = i : P (B_{i}) > 0 \sum P (A ∣ B_{i}) P (B_{i}) .

Indeed,

A

A \cap B_{i}

, and the conditional probability formula gives each positive-probability term. Zero-probability cells contribute zero; their conditionals need not be defined by a ratio. If all cells have positive probability, the sum simply runs over every

i \in I

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