Transition Probability Matrix

However, using a tree diagram also has its limitations: if we want to calculate the probability after a month or even half a year, the tree diagram method will no longer be efficient. Therefore, mathematicians adopted the calculation method using Matrix. The matrix below is called the “transition probability matrix”.

$ \left(\begin{array}{cccc}1&2&3&4\\5&6&7&8\end{array}\right) $