$E_1$ and $E_2$ are two independent events of a random experiment such that $P\left(E_1\right)=\frac{1}{2}$ and $P\left(E_1 \cup E_2\right)=\frac{2}{3}$. Then, match the items of List I with the items of List II.

$$ \begin{array}{lll} \hline & \text { List I } & \text { List II } \\ \hline \text { (A) } & P\left(E_2\right) & \text { (i) }1/2 \\ \hline \text { (B) } & P\left(E_1 / E_2\right) & \text { (ii) } 5 / 6 \\ \hline \text { (C) } & P\left(E_2 / E_1\right) & \text { (iii) } 1 / 3 \\ \hline \text { (D) } & P\left(E_1 \cup E_2\right) & \text { (iv) } 1 / 6 \\ \hline & & \text { (v) } 2 / 3 \\ \hline \end{array} $$

A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from first bag and two balls from the second bag at random. The probability that out of the three, two are black and one is red, is

If a random variable $X$ has the following probability distribution, then its variance is nearly

$$ \begin{array}{clllllll} \hline X=x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline P(X=x) & 0.05 & 0.1 & 2 K & 0 & 0.3 & K & 0.1 \\ \hline \end{array} $$