A bag contains $5$ white, $7$ red $8$ black balls. If four balls are drawn one by one with replacement, what is the probability that all are white

A bag contains $5$ white, $7$ red $8$ black balls. If four balls are drawn one by one with replacement, the probability that at least one is white is $\frac{k}{256}$. Find the value of $k$.

A policeman fires $6$ bullets at a burglar. The probability that the burglar will be hit by a bullet is $0.6$. What is the probability that burglar is still unhurt?

A die is tossed thrice. A success is $1$ or $6$ on a toss. Find the mean and variance of successes.

A die is thrown $100$ times. Getting an even number is considered a success. Find the mean and variance of success.

Determine the binomial distribution whose mean is $9$ and variance is $6$?

Find the binomial distribution whose mean is $5$ and variance is $2.5$.

The mean and variance of a binomial distribution are $4$ and $\left(\frac{4}{3}\right)$ respectively. Find $\mathrm{P}(\mathrm{X}\ge 1)$.

For a binomial distribution, the mean is $6$ and the standard deviation is $\sqrt{2}$. If the probability of getting $5$ successes is ${}^{9}C_5\frac{k}{3^9}$, then find the value of $k$.