In the Dark Ages, Harvard, Dartmouth, and Yale admitted only male students.

Assume at that time, 80 percent of the sons of Harvard men went to Harvard and the rest

went to Yale, 40 percent of the sons of Yale men went to Yale, and the rest split evenly

between Harvard and Dartmouth; and of the sons of Dartmouth men, 70 percent went to

Dartmouth, 20 percent to Harvard, and 10 percent to Yale.

Find the probability that the grandson of a man from Harvard went to Harvard, and the similar

probabilities that the grandsons of men who went to Dartmouth and Yale also went to

Dartmouth and Yale.