 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/8/a/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

For

p = 3/4

, the five probabilities in increasing white-egg order are

(1, 12, 54, 108, 81) /256

. The largest is

108/256 = 27/64

, so the most common nest has three white eggs and one brown egg,

W_{3} B_{1}

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