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

The mean and variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of exactly two successes is

For Binomial distribution $B \left(10, \frac{1}{2} \right)$,if $P(X \leq 2) = m \left( \frac{1}{2} \right)^{10}$,then $m =$ . . . . . . .

$A$ target is to be destroyed in a bombing exercise and there is a $75 \%$ chance that a bomb will hit the target. Assuming that two direct hits are required to destroy the target completely,the minimum number of bombs to be dropped in order that the probability of destroying the target is not less than $99 \%$,is

For a binomial variate $X$,if $n=4$ and $P(X=4)=6 P(X=2)$,then the value of $p$ is

There are $6$ boxes labelled $B_1, B_2, \ldots, B_6$. In each trial,two fair dice $D_1, D_2$ are thrown. If $D_1$ shows $j$ and $D_2$ shows $k$,then $j$ balls are put into the box $B_k$. After $n$ trials,what is the probability that $B_1$ contains at most one ball?