If $15$ coins are tossed,then the probability of getting $10$ heads is:

Let $\lim _{t \rightarrow 0}(1+5 t)^{\frac{1}{t}}=K$ and $X$ be the random variable representing the number of successes in $100$ independent trials. If the probability of success in each trial is $0.05$, then the probability of getting at least one success is

If $X$ and $Y$ are two independent binomial variates,satisfying $B(10, 1/2)$ and $B(8, 1/2)$ respectively,then the probability $P(X + Y = 2)$ is

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(n_1, 0.5)$ and $Y \sim B(n_2, 0.4)$. If the variance of both $X$ and $Y$ is $6$,then $\sqrt{n_1+n_2}=$

Four fair dice are thrown independently $27$ times. Then the expected number of times,at least two dice show up a three or a five,is

The mean and the variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of $2$ successes is