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:

For a Binomial distribution,$n=6$,if $9 P(X=4)=P(X=2)$,then $q=$

On average, one out of $10$ persons is busy. If $6$ persons are selected at random, then the probability that at least $5$ of them will be busy is...

$A$ fair die with faces $1, 2, 3, 4, 5,$ and $6$ is tossed $4$ times. What is the probability that in all $4$ tosses,the value obtained is not less than $2$ and not greater than $5$ (in $/81$)?

$A$ discrete random variable $X$ has the distribution $B(15, p)$. Given that $\operatorname{Var}(X) = 3.15$. Then,the two possible values of $p$ are

An urn contains $25$ balls,of which $10$ balls bear a mark $'X'$ and the remaining $15$ bear a mark $'Y'$. $A$ ball is drawn at random from the urn,its mark is noted down,and it is replaced. If $6$ balls are drawn in this way,find the probability that at least one ball will bear the $'Y'$ mark.