An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is

If a variable takes values $0, 1, 2, ..., n$ with frequencies proportional to the binomial coefficients $^nC_0, ^nC_1, ..., ^nC_n$,find the mean of the distribution.

If a random variable $X$ takes the values $x_1, x_2, x_3, \ldots, x_{100}$ with probability $P(X=x_i) = K i(i+1)$,then $200 K=$

In a book of $500$ pages, it is found that there are $250$ typing errors. Assume that Poisson law holds for the number of errors per page. Then, the probability that a random sample of $2$ pages will contain no error, 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 value of the constant $c$,so that $P(x)=c\left(\frac{2}{3}\right)^{x}$,$x=1,2,3, \ldots$ is the probability distribution function of a discrete random variable $X$ is