 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/ii/paper-3/27j/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

At gross rate

R = 5/4

q_{0} = \frac{( 5/4 ) 15 - 12}{30 - 12} = \frac{3}{8}, q_{u} = \frac{( 5/4 ) 30 - 36}{45 - 36} = \frac{1}{6}, q_{d} = \frac{( 5/4 ) 12 - 10}{16 - 10} = \frac{5}{6} .

All lie strictly between zero and one. The four terminal path probabilities are

1/16, 5/16, 25/48, 5/48

in the order good-good, good-bad, bad-good, bad-bad.

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