If the mean and standard deviation of a binomial distribution are $20$ and $4$,respectively,then the number of trials is $.......$

If $X$ is a binomial variate with the range $\{0, 1, 2, 3, 4, 5, 6\}$ and $P(X=2) = 4 P(X=4)$,then the parameter $p$ of $X$ is

$A$ 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 a fair coin is tossed $10$ times,find the probability of getting at least six heads.

If the sum of mean and variance of a Binomial Distribution is $\frac{15}{2}$ for $10$ trials,then the variance is (in $.5$)

It is observed that $25 \%$ of the cases related to child labour reported to the police station are solved. If $6$ new cases are reported,then the probability that at least $5$ of them will be solved is