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

Multiple Choice

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) $[0.4750 .525]$