Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. The mean of the number of kings is:

For an initial screening of an entrance exam,a candidate is given $50$ problems to solve. If the probability that the candidate can solve any problem is $\frac{4}{5}$,then the probability that he is unable to solve less than $2$ problems is:

Let $X \sim B(6, 1/2)$,then $P[|X-4| \leq 2]$ is

An unbiased coin is tossed $8$ times. The probability that head appears consecutively at least $5$ times is

$A$ man takes a step forward with probability $0.4$ and backward with probability $0.6$. The probability that at the end of eleven steps he is one step away from the starting point is

The sum and product of the mean and variance of a binomial distribution are $82.5$ and $1350$ respectively. The number of trials in the binomial distribution is: