$A$ die is thrown $100$ times. The standard deviation of getting an even number is:

If a random variable $X$ follows the Binomial distribution $B(10, p)$ such that $5 P(X=0) = P(X=1)$,then the value of $\frac{P(X=5)}{P(X=6)}$ is equal to

The probability that a student gets distinction in a Mathematics test is $\frac{2}{3}$. If five such tests are conducted over a certain period of time,then the probability that he gets distinction in at least $3$ tests is

If $X \sim B(4, p)$ and $P(X=0)=\frac{16}{81}$,then $P(X=4)=$

Consider $5$ independent Bernoulli trials,each with a probability of success $p$. If the probability of at least one failure is greater than or equal to $31/32$,then in which interval does $p$ lie?

$A$ dice is thrown $(2n + 1)$ times. The probability of getting $1, 3$ or $4$ at most $n$ times is: