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

The probability of guessing correctly at least $7$ out of $10$ answers in a "True" or "False" test 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 binomial distribution $B(n, p = \frac{1}{4})$,if the probability of at least one success is greater than or equal to $\frac{9}{10}$,then $n$ is greater than:

$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,the probability distribution of $X$ is given by:

One hundred identical coins,each with probability $p$ of showing up heads,are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is