3. [10 marks] Assume that a person's profession can be classified as professional, skilled labourer, or unskilled labourer. Assume that all families are single parent families. Assume that, of the children of professionals, 80% are professional, 10% are skilled labourers, and 10% are unskilled labourers. In the case of children of skilled laborers, 60% are skilled labourers, 20% are professional, and 20% are unskilled. Finally, in the case of unskilled labourers, 50% of the children are unskilled labourers, and 25% each are in the other two categories. Assume that every worker has at least one child and form a Markov chain by following the profession of a randomly chosen child of a given worker through several generations. Set up the matrix of transition probabilities. Currently 35% of the workers are professional, 45% are skilled labourers and the remaining workers are unskilled labourers. a) Given the initial conditions above, is steady state ever reached? If so, what percentages of workers are at each category at steady state? If steady state is not reached explain why. b) Find the probability that a randomly chosen child, grandchild and great-grandchild of a skilled labourer are professionals