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

In a box containing $100$ bulbs,$10$ are defective. The probability that out of a sample of $5$ bulbs,none is defective is

If $X$ is a binomial variate with mean $6$ and variance $2$,then the value of $P(5 \leq X \leq 7)$ is

In a bombing attack,there is a $50 \%$ chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs that must be dropped to ensure that there is at least a $99 \%$ chance of completely destroying the target is:

$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,the probability distribution of $X$ is given by:

In a binomial distribution,if $n=4$ and $P(X=0)=\frac{16}{81}$,then $P(X=4)=$