On a multiple choice examination with three possible answers for each of the five questions,what is the probability that a candidate would get four or more correct answers just by guessing?

$A$ fair coin is tossed $n$ times. If the probability that head occurs $6$ times is equal to the probability that head occurs $8$ times,then $n$ is equal to:

For a binomial variate $X$ with parameters $n=5$ and $p=\frac{3}{4}$. If $\alpha=\frac{1}{9} P(X \geq 3)$ and $\beta=P(X \leq 2)$,then $256(\beta-\alpha)=$

$A$ random experiment is conducted five times. If the number of successes of the experiment follows a binomial distribution such that the difference between the mean and variance of the successes is $\frac{5}{9}$, then the probability of getting at most two successes is

If a random variable $X$ follows the Binomial distribution $B(33, p)$ such that $3P(X=0) = P(X=1)$,then the value of $\frac{P(X=15)}{P(X=18)} - \frac{P(X=16)}{P(X=17)}$ is equal to

$A$ random variable $X$ follows the binomial distribution and $X \sim B(n, 0.3)$. If the mean of $X$ is three times as large as the standard deviation of $X$,then $n=$