= Solution
Take “cousins” to <mean> <first cousins> with unrelated, outbred founders and unrelated spouses in the intervening generation. Interpret a <homozygous> chromosome as two copies <identical by descent>, and first use an idealization of independent, nonrecombining <chromosome> blocks. Ordinary sequence <homozygosity> is a different quantity: unrelated copies can have the same allele, so its <probability> also requires <allele frequencies>. Similarly, identity of an entire recombining chromosome requires a <genetic map>, not just a pedigree.
At a single autosomal locus, the <probability> of <autozygosity> in their child is the parents' <kinship coefficient>. Each of the two common grandparents contributes a path of length two from each parent, with <probability> $(1/2)^{2+2+1}$. Thus the <first-cousin inbreeding coefficient> is
$$
F=2(1/2)^5=1/16.
$$
If there are $L$ independent autosomal blocks, the <probability> that none is autozygous is $(1-F)^L$. Hence the usual 23-block idealization gives
$$
\boxed{\Pr(\text{at least one autozygous block})=1-(15/16)^{23}.}
$$
The exponent describes the stated independent-block approximation; it is not a claim that all 23 human chromosome pairs inherit like autosomes.
Humans have 22 autosomal pairs. A son has one X and one Y and cannot have two homologous X copies. A daughter can have an autozygous X, with <probability> $F_X$ determined by the <sex-linked cousin kinship> calculation in part (b). Thus a sex-aware version is
$$
\boxed{\Pr(\text{at least one autozygous paired block})=1-(15/16)^{22}(1-p_DF_X),}
$$
where $p_D$ is the <probability> of a daughter, or is one or zero for a specified daughter's or son's sex. The <independent assortment> approximation applies between the autosomes and the X. Opposite-sex parentage alone does not determine $F_X$: the parents may be cousins through their mothers, their fathers or one of each. Without these pedigree and chromosome-block assumptions, the wording does not specify a unique <probability> of an entire homozygous human chromosome.
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