 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2017/prelims/mathematics-iii/5/b/ii/solution

Let

q_{n} = P (M_{n} = Y)

p_{n} = \frac{1}{2} p_{n - 1} + \frac{3}{8} q_{n - 1}, q_{n - 1} = \frac{1}{2} p_{n - 2} (n \geq 2) .

The second equality holds because

Y

can only be reached from

X

. Eliminating

q_{n - 1}

16 p_{n} = 8 p_{n - 1} + 3 p_{n - 2}, n \geq 2.

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