 Solution

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

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

E, F

have parents

G, D

. Since

G

is noninbred,

ϕ_{GG} = 1/2

, whereas

ϕ_{DD} = 5/8

and

ϕ_{G D} = 1/8

. Applying the parental kinship coefficient recursion to both siblings gives

ϕ_{EF} = \frac{ϕ _{GG} + 2 ϕ _{G D} + ϕ _{DD}}{4} = \frac{1/2 + 2 ( 1/8 ) + 5/8}{4} = \frac{11}{32} .

The familiar outbred-sibling value

1/4

does not apply to this inbred pedigree.

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