Consider $5$ independent Bernoulli trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$,then $p$ lies in the interval:

Out of $100$ people selected at random,$10$ have a common cold. If five persons are selected at random from the group,then the probability that at most one person will have a common cold 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:

If three dice are thrown together,then the probability of getting $5$ on at least one of them 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

If $X$ follows the Binomial distribution with parameters $n=6$ and $p$ and $9 P(X=4) = P(X=2)$,then $p$ is