If the initial occurrence of those genotypes in the population is 0.5 for DD, 0.4 for Dr, and 0.1 for rr, find the distribution (probability) of each type after the first and second generations.
For species that reproduce sexually, characteristics are determined by a gene from each parent. Suppose that for a certain trait there are two possible genes available from each parent: a dominant gene D and a recessive gene r. Then the different gene combinations (called genotypes) for the offspring are DD, Dr, rD, and rr, where Dr and rD produce the same trait. Suppose further that these genotypes are the states of a Markov chain with the following transition matrix.

Offspring genotype DD Parent genotype Dr rr DD 0.7 0.3 0 Dr 0.35 0.5 0.15 0.7 0.3 rr