$A$ 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:

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively,then what is the probability that $X \geq 1$?

$A$ student appeared in an examination consisting of $8$ true-false type questions. The student guesses the answers with equal probability. The smallest value of $n$,so that the probability of guessing at least $n$ correct answers is less than $\frac{1}{2}$,is:

It is observed that $30 \%$ of the students appearing for a certain entrance test are science students. If $5$ students are randomly selected from this group,the probability of having $2$ science students among these students is

During the winter months,in a certain village in Scotland,the probability of a day having severe fog is $0.6$. The probability that in a given week there will be exactly two days with severe fog is:

If $X \sim B(4, p)$ and $2 P(X=3)=3 P(X=2)$,then the value of $p$ is: