$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all $6$ questions such that exactly $4$ of the answers are correct is:

Let $X$ be a binomial variate with parameters $n=6$ and $p$. If $4 P(X=4)=P(X=2)$, then $p$ equals

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting a head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$,respectively. Suppose $\alpha$ is the number of heads that appear when $C_1$ is tossed twice,independently,and $\beta$ is the number of heads that appear when $C_2$ is tossed twice,independently. Then,the probability that the roots of the quadratic polynomial $x^2 - \alpha x + \beta$ are real and equal is:

On average, one out of $10$ persons is busy. If $6$ persons are selected at random, then the probability that at least $5$ of them will be busy is...

If the probability that a student is not a swimmer is $\frac{1}{5}$,then the probability that out of $5$ students one is a swimmer is

If a Bernoulli trial is conducted $n$ times,then which one of the following is not suitable to use Poisson distribution?
$(i)$ Each trial results in two mutually exclusive outcomes namely success,failure.
(ii) The number $n$ of such trials is sufficiently large.
(iii) The trials are independent of each other.
(iv) The probability $p$ of success in each trial is very large.