 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/undated/prelims/mathematics-iii-resit/4/b/iii/solution

There are three even faces, so

P (A) = 1/2

. The sum is even precisely when both faces have the same parity, giving

9 + 9 = 18

outcomes and

P (B) = 1/2

. Both

A

and

B

occur precisely when both faces are even, giving nine outcomes. Therefore

P (A \cap B) = \frac{9}{36} = \frac{1}{4} = P (A) P (B) .

Thus

A

and

B

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