If the standard deviation of the random variable $X$ is $\sqrt{3pq}$ and the mean is $3p$,then $E(X^2) = . . . . . . .$

If $12$ identical balls are to be placed in $3$ distinct boxes,then the probability that one of the boxes contains exactly $3$ balls is:

Suppose $X$ follows a binomial distribution with parameters $n$ and $p$,where $0 < p < 1$. If $\frac{P(X=r)}{P(X=n-r)}$ is independent of $n$ for every $r$,then $p$ is equal to

If $X$ is a binomial variable with range $\{0, 1, 2, 3, 4\}$ and $P(X=3) = 3P(X=4)$,then the parameter $p$ of the binomial distribution is:

In a university campus, the probability that a person chosen at random is an engineering student is $\frac{1}{5}$. The probability of having at most two engineering students in a sample of $8$ people is:

$A$ coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed $3$ times,then the probability of getting two tails and one head is-