For a binomial variate $X$ with $n=6$,if $P(X=2)=9 P(X=4)$,then its variance is

Numbers are selected at random,one at a time from the two-digit numbers $00, 01, 02, \dots, 99$ with replacement. An event $E$ occurs only if the product of the two digits of a selected number is $24$. If four numbers are selected,then the probability that the event $E$ occurs at least $3$ times is:

The variance of the following probability distribution of $X$ is given by:
$X: 0, 1, 2, 3$
$P(X): q^3, 3pq^2, 3p^2q, p^3$
where $0 < p < 1$ and $q = 1 - p$.

$A$ die is thrown $5$ times. Getting an odd number is considered a success. Find the variance of the distribution of successes.

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:

If $X$ is a binomial variate with the range $\{0, 1, 2, 3, 4, 5, 6\}$ and $P(X=2) = 4 P(X=4)$,then the parameter $p$ of $X$ is