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(D) The inheritance of grain color in wheat is an example of polygenic inheritance involving $3$ pairs of genes $(n=3)$.In this case,the parental phen

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$2/64$

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(D) The inheritance of grain color in wheat is an example of polygenic inheritance involving $3$ pairs of genes $(n=3)$.In this case,the parental phenotypes are extreme: one is dark red (all dominant alleles,$AABBCC$) and the other is white (all recessive alleles,$aabbcc$).According to the binomial expansion $(1/2 + 1/2)^{2n}$,where $n=3$,the total number of combinations is $2^{2n} = 2^6 = 64$.The parental phenotypes (extreme red and extreme white) appear only when all alleles are dominant or all are recessive.The probability of obtaining the genotype $AABBCC$ is $(1/4)^3 = 1/64$.The probability of obtaining the genotype $aabbcc$ is $(1/4)^3 = 1/64$.Therefore,the total fraction of offspring resembling the parental phenotypes is $1/64 + 1/64 = 2/64$.

The grain color in wheat is controlled by three pairs of polygenes. When a red-grained wheat variety is crossed with a white-grained variety,an $F_1$ hybrid is produced. When the $F_1$ hybrid is self-pollinated,what fraction of the $F_2$ generation will resemble the parental phenotypes?

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