The probability that a student is not a swimmer is $\frac{1}{5}$. The probability that out of 5 students selected at random 4 are swimmers is

A player tosses two coins. He wins ₹ 10 , if 2 heads appears, ₹ 5 , if one head appear and ₹ 2 if no head appears. Then variance of winning amount is

Consider the probability distribution

$$ \begin{array}{|l|l|l|l|l|l|} \hline \mathrm{X}=x & 1 & 2 & 3 & 4 & 5 \\ \hline \mathrm{P}(\mathrm{X}=x) & \mathrm{K} & 2 \mathrm{~K} & \mathrm{~K}^2 & 2 \mathrm{~K} & 5 \mathrm{~K}^2 \\ \hline \end{array} $$

Then the value of $\mathrm{P}(\mathrm{X}>2)$ is

Let X denote the number of hours you study on a Sunday. It is known that

$$ \mathrm{P}(\mathrm{X}=x)=\left\{\begin{array}{cc} 0.1 & , \text { if } x=0 \\ \mathrm{k} x & , \text { if } x=1 \text { or } 2 \\ \mathrm{k}(5-x) & , \text { if } x=3 \text { or } 4 \\ 0 & , \text { otherwise } \end{array}\right. $$

where k is constant. Then the probability that you study at least two hours on a Sunday is