At one liberal arts college, students are classified as humanities majors, science majors, or undecided. The chances are 10%

Question

At one liberal arts college, students are classified as humanities majors, science majors, or undecided. The chances are 10% that a humanities major will change to a
science major from one year to the next, and 45% that a humanities major will change to undecided. A science major will change to humanities with probability 0.25,
and to undecided with probability 0.25. An undecided will switch to humanities or science with ptobabilities of 0.30 and 0.40, respectively. Complete parts (a) and (b)
below.
(a) Find the long-range prediction for the fraction of students in each of these three majors.
First, find the transition matrix P. Let the first state be that a student is a humanities major, the second that a student is a science major, and the third state that a
student is undecided.

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