Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 05 (a)/Solution 1

Coin head and coin tail are equally distributed with possibility $1/2$. If the driver starts at B for example, the possibility that he stays at B is equal to coin head, which is $1/2$. If he gets coin tail, he can move to A, C, or D. The possibility for each one is $1/2{\text{(get coin head)}}\times 1/3{\text{(choose one out of there)}}$. Based on this, we get the probability transition matrix

Answer: $P=\color {blue}{\begin{bmatrix}1/2&1/6&1/6&0\\1/4&1/2&1/6&1/4\\1/4&1/6&1/2&1/4\\0&1/6&1/6&1/2\end{bmatrix}}$