Consider two events $E_1$ and $E_2$ such that probability of $E_1$, $P_r[E_1]=\frac{1}{2}$, probability of $E_2$, $P_r[E_{2}]=\frac{1}{3}$, and probability of $E_1$, and $E_2$, $P_r[E_1 \: and \: E_2] = \frac{1}{5}$. Which of the following statements is/are true?

$P_r[E_1\: \text{or} \:E_2] \text{ is } \frac{2}{3}$

Events $E_1$ and $E_2$ are independent

Events $E_1$ and $E_2$ are not independent

$P_r \left[{E_1}\mid{E_2} \right] = \frac{4}{5}$