Assume (naively) that a person's job can be classified as professional, skilled, or unskilled. Assume that, of the children of professional parents, 80 percent are professional, 10 percent are skilled, and 10 percent are unskilled. In the case of children of skilled, 60 percent are skilled, 20 percent are professional, and 20 percent are unskilled. Finally, in the case of unskilled, 50 percent of the children are unskilled, and 25 percent each are in the other two categories. Assume that every family has at least one child.
a) Form a Markov chain by following the job of a randomly chosen child of a given family through several generations. Set up the matrix of transition probabilities.
b) Find the probability that a randomly chosen grandchild of an unskilled worker is a professional.