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

$A$ binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is

For an initial screening of an admission test,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 two problems is

The probability of success $p$ for the Binomial distribution satisfying the relation $4 P(X=4) = P(X=2)$ with parameter $n=6$ is

$A$ dice is thrown $(2n + 1)$ times. The probability of getting $1, 3$ or $4$ at most $n$ times is:

If the mean and variance of a binomial variable $X$ are $2$ and $1$ respectively, then $P(X \geq 1)$ is equal to