If the probability that an individual will suffer a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ individuals suffer a bad reaction is

If $X$ is a Poisson variate with mean $2$,then $P\left(X>\frac{3}{2}\right)=$

$A$ bag contains $4$ white and $6$ black balls. Three balls are drawn at random from the bag. Let $X$ be the number of white balls among the drawn balls. If $\sigma^{2}$ is the variance of $X$,then $100 \sigma^{2}$ is equal to.

$A$ random variable $X$ has the following probability distribution:
| $x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
|---|---|---|---|---|---|---|---|---|
| $P(x)$ | $0.15$ | $0.23$ | $0.12$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
For the events $E = \{x \text{ is a prime number}\}$ and $F = \{x < 4\}$,the probability $P(E \cup F)$ is:

The probability distribution of a random variable $X$ is given below. Then, the standard deviation of $X$ is

$X=x_i$	$2$	$3$	$5$	$7$	$12$
$P(X=x_i)$	$3k$	$k$	$k$	$2k$	$k$

If $P(X=x)=k\left(\frac{3}{8}\right)^{X}, x=1,2,3, \ldots$ is the probability distribution function of a discrete random variable $X$,then $k=$