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 $C$.

Two balls are drawn at random from a bag containing $5$ black balls and $3$ white balls. If the random variable $X$ denotes the number of white balls drawn,then the mean of $X$ is

If a die is thrown at random,then the expectation of the number on it is

$A$ die is loaded in such a way that each odd number is twice as likely to occur as each even number. If $E$ is the event that a number greater than or equal to $4$ occurs on a single toss of the die,then $P(E)$ is equal to:

The random variable $X$ has a probability distribution $P(X)$ of the following form,where $k$ is some number:
$P(X) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$
Determine the value of $k$.

The expected value of the sum of the two numbers obtained on the uppermost faces,when two fair dice are rolled,is