$A$ multiple-choice examination consists of $5$ questions. Each question has $3$ alternative answers,of which only $1$ is correct. What is the probability that a student will get $4$ or more correct answers?

If a random variable $X$ follows the Binomial distribution $B(33, p)$ such that $3 P(X=0) = P(X=1)$,then the variance of $X$ is

$A$ person fails $4$ times in a game when he plays $9$ times. If he plays $15$ times, the probability of having success at most one is

Let $X$ have a binomial distribution $B(n, p)$ such that the sum and the product of the mean and variance of $X$ are $24$ and $128$ respectively. If $P(X > n - 3) = \frac{k}{2^n}$,then $k$ is equal to.

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. Then the probability distribution of the number of kings is:

$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,the probability distribution of $X$ is given by: