Find the requested long-range probabilities based on the transition matrix or data given.
-At a liberal arts college, students are classified as humanities or science majors. There is a probability of 0.8 that a humanities major will change to science and of 0.3 that a science major will change to humanities. Find the long-range prediction for the proportion of students in each major.
A) $[0.7270 .273]$
B) $[0.2000 .800]$
C) $[0.2730 .727]$
D) $\left[\begin{array}{ll}0.190 & 0.810\end{array}\right]$

Question

Quizplus · Accepted Answer

The long-range probabilities can be found by solving the system of equations derived from the transition matrix. The equilibrium state is reached when the probabilities stabilize, leading to approximately 27.3% humanities and 72.7% science majors.

Find the Requested Long-Range Probabilities Based on the Transition Matrix [0.7270.273][0.7270 .273][0.7270.273]

Find the Requested Long-Range Probabilities Based on the Transition Matrix $[0.7270 .273]$