 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/i/solution

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

Assuming the egg colours are independent with the same probability

p

, the number of white eggs has the binomial distribution with four trials. The possibilities are

Contents	Probability	$W_{0} B_{4}$	$(1 - p)^{4}$	$W_{1} B_{3}$	$4 p (1 - p)^{3}$	$W_{2} B_{2}$	$6 p^{2} (1 - p)^{2}$	$W_{3} B_{1}$	$4 p^{3} (1 - p)$	$W_{4} B_{0}$	$p^{4}$

The binomial coefficients count which eggs are white. Marginal colour probabilities alone would not determine nest probabilities without the independence assumption.

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