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 $\frac{1}{2}$ and probability of occurrence of 0 at the odd place be $\frac{1}{3}$. Then the probability that ' 10 ' is followed by '01' is equal to :
Correct Option: , 4
$\begin{array}{cccc}1 & 0 & 0 & 1 \\ \text { odd place even place } & \text { odd place } & \text { even place }\end{array}$
or
$\begin{array}{ccc}1 & 0 & 0 \\ \text { even place odd place } & \text { even place odd place }\end{array}$
$\Rightarrow\left(\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2} \cdot \frac{2}{3}\right)+\left(\frac{2}{2} \cdot \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2}\right)$
$\Rightarrow \frac{1}{9}$
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