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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?

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

2. Events $E_1$ and $E_2$ are independent

3. Events $E_1$ and $E_2$ are not independent

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

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Answer - $C$

If events $E_1$ and $E_2$ are independent then $P[E_1$ and $E_2]$ = $P[E_1]\times P[E_2]$ which is not the case here.
edited