In a certain two-year college, of those who were freshmen (F) during a particular year, 70% became sophomores (S) the next year and 30% dropped out (D). Of those who were sophomores during a particular year, 90% graduated (G) by the next year and 10% dropped out.
(a) Set up the absorbing stochastic matrix for this transition, with the states D, G, F, S listed in this order.
$\begin{bmatrix}
1 & 0 & .3 & .1 \\
0 & 1 & 0 & .9 \\
0 & 0 & 0 & 0 \\
0 & 0 & .7 & 0
\end{bmatrix}$
(b) Find the stable matrix.
(c) Find the probability that an entering freshman will eventually graduate.
0.63
