 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2003/iii/paper-40/6/b/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

The founder

C

is unrelated to the descendants of

A, B

, while the kinship coefficient between

D

and its parents' sibling

U

ϕ_{D U} = \frac{1}{2} (ϕ_{V U} + ϕ_{W U}) = \frac{1}{4} .

G

has parents

C, U

D, G

ϕ_{D G} = \frac{1}{2} (ϕ_{D C} + ϕ_{D U}) = \frac{1}{2} (0 + \frac{1}{4}) = \frac{1}{8} .

The parents of

E

are

D, G

, so

F_{E} = ϕ_{D G} = \frac{1}{8} .

The same calculation gives

F_{F} = 1/8

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