Two individuals heterozygous at four genes are crossed. What proportion of offspring are homozygous recessive at all four?

1. Take the genes one at a time, since all four sort independently. 2. For any one gene, a heterozygote cross gives 1 homozygous dominant to 2 heterozygous to 1 homozygous recessive. 3. The homozygous recessive fraction for that gene is therefore 1/4. 4. The question asks for homozygous recessive at gene one and gene two and gene three and gene four. 5. The repeated word and signals the product rule, so multiply four quarters together. 6. One quarter to the fourth power is 1 over 256. 7. So 1/256 of the offspring are quadruply homozygous recessive. 8. The value 1/16 would be the answer for two genes and 1/64 for three, so both stop short. _Source: OpenStax Biology (1st ed., CC BY 4.0), Ch 12 "Mendel's Experiments and Heredity", section 12.3 Laws of Inheritance_