The probability distribution of a discrete random variable $X$ is given by the table below:

$X$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$k$	$2k$	$4k$	$k$

If $a = P(X < 3)$ and $b = P(2 < X < 4)$,then:

If the probability distribution is given by $P(x) = C \binom{4}{x}$ for $x = 0, 1, 2, 3, 4$,then find the value of $C$.

If the probability that an individual will suffer a reaction from an injection of a drug is $0.001$, then the probability that out of $2000$ individuals having that injection, more than $2$ individuals will suffer a reaction, is

Suppose that a random variable $X$ follows a Poisson distribution. If $P(X=1) = P(X=2)$, then $P(X=5)$ is equal to:

$A$ typist claims that he prepares a typed page with typo errors of $1$ per $10$ pages. In a typing assignment of $40$ pages, if the probability that the typo errors are at most $2$ is $p$, then $e^2 p=$

The probability distribution of $X$ is
$\begin{array}{|c|c|c|c|c|} \hline X & 0 & 1 & 2 & 3 \\ \hline P(X) & 0.3 & k & 2k & 2k \\ \hline \end{array}$
Find the value of $k$.