 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/7/a/ii/solution

Since the

B_{i}

A \cap B_{i}

are pairwise disjoint and their set union is

A

P (A) = \sum_{i = 1}^{\infty} P (A \cap B_{i}) = i = 1 \sum \infty P (A ∣ B_{i}) P (B_{i}) .

Every ratio is legitimate because each

P (B_{i}) > 0

. This proves the countable law of total probability.

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