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

X = x	1	3	5	2
P(X = x)	$3 K^2$	K	$K^2$	2K

The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. IfP $(X > 1)=1-K\left(\frac{3}{5}\right)^{7}$, then $5 K=$

If three numbers are randomly selected from the set $\{1,2,3, \ldots \ldots 50\}$, then the probability that they are in arithmetic progression is

The probability that exactly 3 heads appear in six tosses of an unbiased coin, given that first three tosses resulted in 2 or more heads is