= Solution
The <kinship coefficient> $\phi_{XY}$ is the <probability> that one <allele> copy sampled uniformly from each of individuals $X,Y$, independently conditional on their copies, is <identical by descent>. The <inbreeding coefficient> $F_X$ is the <probability> that the two homologous <allele> copies within $X$ are <identical by descent>. For distinct offspring and older individual, <Mendelian segregation> gives
$$
\phi_{XY}=\tfrac12(\phi_{P_XY}+\phi_{M_XY}),\qquad F_X=\phi_{P_XM_X},\qquad \phi_{XX}=\tfrac12(1+F_X).
$$
For the last identity, two independent selections choose the same copy with <probability> $1/2$, and choose distinct copies with <probability> $1/2$, in which case identity has <probability> $F_X$. \b[An unrelated, noninbred founder has $F=0$ and self-kinship $1/2$], while distinct such founders have zero mutual <kinship coefficient>. The source's statement of zero founder kinship must be read as zero kinship between distinct founders; zero self-kinship would contradict the definition.
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