If a matrix is chosen at random from the set of all $3 \times 3$ non-zero matrices whose entries are the elements of the set $\{-1,0,1\}$, then the probability that the matrix is skew-symmetric is

A boy throws an unbiased die. Whenever he gets 1 on the die he has a further chance to throw it once again immediately. The probability that the boy gets a score of 7 in this process is

There are 10 coins in a box out of which 8 are normal and the remaining are with heads on both sides. A coin is chosen at random from the box and tossed 6 times. If it shows heads each time, then the probability that the selected coin has head on both sides is

$$ \text { A random variable } X \text { has the following distribution, } $$

$$ \begin{array}{lllllll} \hline X=x_i & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline P\left(X=x_i\right) & 0.1 & k & 0.2 & 2 k & 3 k & k \\ \hline \end{array} $$

Then, the variance of this distribution is