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. Rex is a brown dog.

(a) Compute the probability that his grandchild is black.

(b) In a long run, what portion of the off-springs is black?