$A$ die is thrown thrice. If getting $1$ or $6$ in a single throw is considered as success, then the variance of the number of successes is

$A$ 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:

The probability that a student is not a swimmer is $\frac{1}{5}$. Then,the probability that out of $5$ students,$4$ are swimmers is . . . . . . .

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$,then $P(|X-3| < 2)=$

The probability of getting $4$ heads in $8$ throws of a coin is:

$A$ fair coin is tossed $9$ times. On each toss, a man predicts that the outcome will be heads. The probability that the number of successful predictions is strictly greater than the number of unsuccessful predictions is...