55. Consider a population of individuals each of whom possesses two genes which can be either type A or type

a. Suppose that in outward appearance type A is dominant and type a is recessive. (That is, an individual will have only the outward characteristics of the recessive gene if its pair is aa.) Suppose that the population has stabilized, and the percentages of individuals having respective gene pairs AA, aa, and Aa are p, q, and r. Call an individual dominant or recessive depending on the outward characteristics it exhibits. Let S11 denote the probability that an offspring of two dominant parents will be recessive; and let S10 denote the probability that the offspring of one dominant and one recessive parent will be recessive. Compute S11 and S10 to show that S11 = S2 10.

(The quantities S10 and S11 are known in the genetics literature as Snyder’s ratios.)