Find the requested long-range probabilities based on the transition matrix or data given.
-In one town there are only two cello teachers. In a given semester, the probability that a student will switch from Carol Mosely to Betty Roberts is 0.5 The probability that a student of Betty Roberts will switch to Carol Mosely is 0.1. Find the long-range prediction for the proportion of students with each teacher.
A) $[0.8330 .167]$
B) $[0.5000 .500]$
C) $[0.1670 .833]$
D) $[0.4750 .525]$

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 proportion of students switching from one teacher to another balances out. Solving the equations, we find that approximately 16.7% of students will be with Carol Mosely and 83.3% with Betty Roberts.

Find the Requested Long-Range Probabilities Based on the Transition Matrix [0.8330.167][0.8330 .167][0.8330.167]

Find the Requested Long-Range Probabilities Based on the Transition Matrix $[0.8330 .167]$