The probability that an event does not happen in one trial is $0.8$. The probability that the event happens at most once in three trials is:

$A$ box contains $24$ identical balls,of which $12$ are white and $12$ are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the $4^{th}$ time on the $7^{th}$ draw is

In a Binomial distribution with $n=4$,if $2 P(X=3)=3 P(X=2)$,then the variance is

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

An unbiased coin is tossed to get $2$ points for turning up a head and $1$ point for the tail. If three unbiased coins are tossed simultaneously, then the probability of getting a total of an odd number of points 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 $n$ for every $r$,then $p$ is equal to