$A$ box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn,one-by-one,with replacement,then the variance of the number of green balls drawn is:

If $X \sim B(n, p)$ then $\frac{P(X=k)}{P(X=k-1)}=$

If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$,then $P(X \leq 2) = $

Let $X$ be a random variable having binomial distribution $B(7, p)$. If $P(X=3) = 5P(X=4)$,then the sum of the mean and the variance of $X$ is

What is the probability of getting an even number exactly $3$ times when a die is thrown $5$ times?

$A$ bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is $p$. Next,four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colour is $q$. If $p : q = m : n$,where $m$ and $n$ are coprime,then $m + n$ is equal to $..........$.