In a Binomial distribution,if $p=q$ and $n \geq 4$,then $2^n P(X=5)=$

If $X \sim B(9, p)$ is a binomial variate satisfying the equation $P(X=3)=P(X=6)$,then $P(X < 3)=$

$A$ shooter can hit a given target with probability $\frac{1}{4}$. She keeps firing a bullet at the target until she hits it successfully three times and then she stops firing. The probability that she fires exactly six bullets lies in the interval

There are $800$ families with four children in each family. Assuming an equal chance for every child to be a boy or a girl,the number of families expected to have children of both sexes is:

The mean and variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of exactly two successes is

An unbiased coin is tossed $8$ times. The probability that head appears consecutively at least $5$ times is