Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 37 / 5 / i / Solution

Under Hardy-Weinberg equilibrium, the two parental allele copies are sampled independently from the same pool. Multiplying their frequencies, and adding the two orderings for a heterozygote, givesTheir sum is $(p+(1-p){)}^2=1$. The genotypes are unordered even though the paternal and maternal transmissions may be distinguished in the calculation.