A study of occupational mobility in a certain community classified occupations as P (professional), WC (white collar), SM (skilled manual), and UM (unskilled manual). Currently, 4% of the adults are P, 20% are WC, 40% are SM, and 36% are UM. Studies predict that, of the children of P parents, 40% become P, 45% become WC, 10% become SM, and 5% become UM. Of the children of WC parents, 20% become P, 60% become WC, 10% become SM, and 10% become UM. Of the children of SM parents, 10% become P, 45% become WC, 30% become SM, and 15% become UM. Of the children of UM parents, 5% become P, 15% become WC, 25% become SM, and 55% become UM.
(a) Set up the 4 × 4 stochastic matrix that describes this situation.
(b) What percent of the children of the current generation will be professionals?
(c) What percent of the grandchildren of the current generation will be professionals?