$A$ die is thrown thrice. If getting $1$ or $6$ in a single throw is considered as success, then the variance of the number of successes is

If the sum and the product of the mean and variance of a binomial distribution are $24$ and $128$ respectively,then the probability of one or two successes is:

The binomial distribution whose mean is $9$ and whose standard deviation is $\frac{3}{2}$ is equal to

$A$ multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is:

For a binomial distribution with mean $6$ and variance $2$,find $P(X \geq 2)$.

For a binomial variate $X$ with $n=6$,if $P(X=4)=\frac{135}{2^{12}}$,then its variance is