$A$ fair die is thrown $4$ times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is ...

$A$ die is rolled $5$ times. Getting an odd number in one trial is considered as a success. The variance of the distribution of successes is

As a business strategy, $20 \%$ of the new internet service subscribers selected randomly receive a special promotion. If a group of $5$ such subscribers signs for the service, then the probability that at least two of them get the special promotion is

In an examination,there are $10$ true-false type questions. Out of $10$,a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k}{4^{10}}$,then $k$ is equal to

If the mean and variance of a binomial variate $X$ are $2$ and $1$ respectively,then the probability that $X$ takes a value greater than $1$ is

Consider $5$ independent Bernoulli trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$,then $p$ lies in the interval: