The following transition matrix, \(T\), models the movement of a species of bird around three different locations, \(M, N\) and \(O\) from one day to the next.
\begin{aligned}
& \quad \ \ \textit{this day} \\
& \quad M \ \ N \ \ \ O\\
T = & \begin{bmatrix}
\frac{1}{3} & 0 & \frac{9}{10} \\
\frac{1}{3} & 1 & \frac{1}{10} \\
\frac{1}{3} & 0 & 0
\end{bmatrix}\begin{array}{l}
M\\
N\\
O
\end{array}\ \ \ next \ day
\end{aligned}
Which one of the following statements best represents what will occur in the long term?
- No birds will remain at location \(M\).
- No birds will remain at location \(N\).
- All of the birds will end up at location \(M\).
- All of the birds will end up at location \(O\).
- An equal number of birds will be at all three locations.