There are four cities, namely, $C_{1}, C_{2}, C_{3}$ and $C_{4}$. The cities are directly connected by four roads as shown in the picture given below, that is, $C_{1}$ is connected with $C_{2}$, $C_{2}$ is connected with $C_{3}, C_{3}$ is connected with $C_{4}$, and $C_{4}$ is connected with $C_{1}$. The probability of any road getting independently blocked is $\frac{1}{3}$. Let $E_{1}$ be the event of travelling from $C_{1}$ to $C_{3}$ via $C_{2}$ and $E_{2}$ be the event of travelling from $C_{1}$ to $C_{3}$ via $C_{4}$. Then, which of the following statements is correct ?
- $\quad P\left(E_{1} \cup E_{2}\right)=\frac{56}{81}$
- $\quad P\left(E_{1} \cup E_{2}\right)=\frac{8}{9}$
- $\quad P\left(E_{1} \mid E_{2}\right) \neq P\left(E_{1}\right)=\frac{4}{9}$
- $\quad P\left(E_{1} \cap E_{2}\right)=0$
