 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability-resit/7/a/ii/solution

Because the

B_{i}

partition the sample space, the events

A \cap B_{i}

are disjoint and their union is

A

P (A) = i = 1 \sum k P (A ∣ B_{i}) P (B_{i}) .

The assumption

P (B_{i}) > 0

ensures that each conditional probability is defined.

 New to topics? Read the docs here!