Find the Requested Long-Range Probabilities Based on the Transition Matrix $\left[\begin{array}{lll}\frac{1}{3} & \frac{1}{3} & \frac{1}{3}\end{array}\right]$

Multiple Choice

Find the requested long-range probabilities based on the transition matrix or data given.
-Weather is classified as fair, cloudy or rainy in a certain place. The probability that it will be fair, cloudy, or rainy on a given day depends on the weather the previous day. The transition matrix is given below. Find the long-range prediction for the proportion of fair, cloudy, and rainy days.

A) $\left[\begin{array}{lll}\frac{1}{3} & \frac{1}{3} & \frac{1}{3}\end{array}\right]$
B) $\left[\begin{array}{lll}\frac{1}{2} & \frac{1}{4} & \frac{1}{4}\end{array}\right]$
C) $[0.49 0.20 0.31]$
D) $[0.49 0.31 0.20]$