Based on the following statements, choose the correct option.

Statement I The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.

Statement II The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112 .

If each of the coefficients $a, b$ and $c$ in the equation $a x^2+b x+c=0$ is determined by throwing a die, then the probability that the equation will have equal roots, is

$A$ and $B$ throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. $A$ wins if he throws 6 before $B$ throws 7 and $B$ wins if he throws 7 before $A$ throws 6 . If $A$ begins then, the probability of his winning is

$E_1$ 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.

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

The correct match is