If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively,then $P(X>1)=$

$A$ fair coin is tossed $2n$ times. What is the probability that the number of heads and tails obtained in these $2n$ trials are not equal?

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$,then $P(X \leq 3)=$

$A$ multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is:

For $k > 0$,calculate the value of $\sum_{x=0}^{\infty} \frac{k^x}{x !} \lim _{n}$ ${\rightarrow \infty} \frac{n !}{(n-x) !}\left(1-\frac{k}{n}\right)^{n-x}\left(\frac{1}{n}\right)^x$.

For a binomial distribution,the mean and variance are $6$ and $4$ respectively. Find the value of $n$.