$A$ die is thrown $5$ times. Getting an odd number is considered a success. Find the variance of the distribution of successes.

The probability of a bomb hitting a bridge is $\frac{1}{2}$ and two direct hits are needed to destroy it. The least number of bombs required so that the probability of the bridge being destroyed is greater than $0.9$ is:

Suppose $X$ follows a binomial distribution with parameters $n$ and $p$,where $0 < p < 1.$ If $\frac{P(X = r)}{P(X = n - r)}$ is independent of $n$ and $r$,then

An experiment succeeds twice as often as it fails. Find the probability that in $4$ trials there will be at least three successes.

$A$ variable $X$ takes values $0, 0, 2, 6, 12, 20, ..., n(n-1)$ with frequencies $^nC_0, ^nC_1, ^nC_2, ^nC_3, ^nC_4, ^nC_5, ..., ^nC_n$, respectively. If the mean of this data is $60$, then its median is:

For a binomial distribution with mean $6$ and variance $2$,the value of $P(X = 8)$ is