The probability distribution of a discrete random variable $X$ is given below

$$ \begin{array}{lllll} \hline X=x & -1 & 0 & 1 & 2 \\ \hline P(X=x) & \frac{1}{3} & \frac{1}{6} & \frac{1}{6} & \frac{1}{3} \\ \hline \end{array} $$

Then, the value of $6 \sum\left(x^2\right) P(X=x)-\operatorname{var}(X)=$

If the average number of accidents occurring at a particular junction on a highway in a week is 5 , then the probability that atmost one accident occurs in a particular week is

An unbiased coin is tossed 8 times. The probability that head appears consecutively at least 5 times is

A box contains twelve balls of which 4 are red, 5 are green and 3 are white. If three balls are drawn at random simultaneously from the box, then the probability that exactly 2 balls have the same colour is