Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be 1/2…

Let a computer program generate only the digits $\displaystyle 0$ and $\displaystyle 1$ to form a string of binary numbers with probability of occurrence of $\displaystyle 0$ at even places be $\displaystyle \frac{1}{2}$ and probability of occurrence of $\displaystyle 0$ at the odd place be $\displaystyle \frac{1}{3}$. Then the probability that ' $\displaystyle 10$ ' is followed by ' $\displaystyle 01$ ' is equal to :