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

If the mean and variance of a binomial variate $X$ are $8$ and $4$ respectively,then $P(X < 3)$ equals to

If five dice are thrown simultaneously, then the probability that at least three of them show the same numbered face is

The probability of success $p$ for the Binomial distribution satisfying the relation $4 P(X=4) = P(X=2)$ with parameter $n=6$ is

In a shelf, there are $3$ mathematics and $2$ physics books. $A$ student takes a book randomly. If he takes a book randomly, successively for $3$ times by replacing the book already taken every time, then the mean of the number of mathematics books, which is treated as a random variable, is:

If $X$ is a binomial variate with the range $\{0, 1, 2, 3, 4, 5, 6\}$ and $P(X=2) = 4 P(X=4)$,then the parameter $p$ of $X$ is