Birth weights can be classified as Low (less than 6 pounds), Average (between 6 and 8 pounds), and High (greater than 8 pounds). Birth weights of female babies tend to be influenced by the birth weights of their mothers. Suppose that this tendency is given by the following matrix:

(a) If the initial distribution of birth weights is given by the matrix

What is the distribution after one generation?
(b) What is the probability that a woman of High birth weight will have a granddaughter of High birth weight? Of Average birth weight?

Mother A .5 25 .2 Daughter A 4 5 .2 .1 25 .6 .4 .4 .2