We can number the states as follows:

1:science fiction;   2: Proust;   3: calculus

With this numbering, the transition matrix is

P = 0 0.75 0.25 0.5 0 0.5 0 1 0 .

Since 17,000 weeks corresponds to a large number of steps, we must calculate the long-term matrix, P.

Using the method in the text, we get

P = 4/17 8/17 5/17 4/17 8/17 5/17 4/17 8/17 5/17 .

Thus, 4/17 of all the books are science fiction in the long term.

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