In a box containing $100$ eggs,$10$ eggs are rotten. The probability that out of a sample of $5$ eggs none is rotten if the sampling is with replacement is

$A$ random variable $X \sim B(n, p)$ follows a binomial distribution with $n = 6$. If $9P(X = 4) = P(X = 2)$, then the probability of success $p$ is:

In a random experiment,two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated $9$ times. If the probability that a sum of $6$ appears at least once is $P_1$ and a sum of $8$ appears at least once is $P_2$,then $P_1 : P_2 =$

For a binomial distribution,the mean and variance are $6$ and $4$ respectively. Find the value of $n$.

The probability that a man fails to hit a target is $\frac{1}{3}$. If he fires $4$ times,then the probability that he hits the target at least thrice is

$A$ coin is tossed $100$ times. What is the probability of getting a tail an odd number of times?