$A$ fair coin is tossed a fixed number of times. If the probability of getting five heads is equal to that of getting seven heads,then the probability of getting four heads is

If $X \sim B(6, p)$ is a binomial variate and $\frac{P(X=4)}{P(X=2)}=\frac{1}{9}$,then $p=$

$A$ student appeared in an examination consisting of $8$ true-false type questions. The student guesses the answers with equal probability. The smallest value of $n$,so that the probability of guessing at least $n$ correct answers is less than $\frac{1}{2}$,is:

On a multiple choice examination with three possible answers for each of the five questions,what is the probability that a candidate would get four or more correct answers just by guessing?

An unbiased die is tossed $500$ times. The standard deviation of getting sixes in these $500$ tosses is

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