Markov chains find direct applications in genetics. Here is an example. An offspring of a black dog is black with probability 0.6 and brown with probability 0.4. An offspring of a brown dog is black with probability 0.2 and brown with probability 0.8. (a) Write the transition probability matrix of this Markov chain. (b) Rex is a brown dog. Compute the probability that his grandchild is black.