The probability that a person will develop immunity after vaccination is $0.8$. If $8$ people are given the vaccine,then the probability that all develop immunity is equal to:

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 . . . . . . .

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:

$A$ coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed $3$ times,then the probability of getting two tails and one head is-

In a Binomial distribution,if $n$ is the number of trials and the mean and variance are $4$ and $3$ respectively,then $2^{32} P\left(X=\frac{n}{2}\right)=$

$A$ and $B$ are two tennis players of equal skill. If they play $4$ games,what is the probability that $A$ wins exactly three games?