If $X \sim B\left(8, \frac{1}{2}\right)$,then $P(|X-4| \leq 2) = $

The sum and product of the mean and variance of a binomial distribution are $82.5$ and $1350$ respectively. The number of trials in the binomial distribution is:

An urn contains $25$ balls of which $10$ balls bear a mark $'X'$ and the remaining $15$ bear a mark $'Y'$. $A$ ball is drawn at random from the urn,its mark is noted down and it is replaced. If $6$ balls are drawn in this way,find the probability that not more than $2$ will bear $'Y'$ mark.

If a fair coin is tossed $10$ times,find the probability of at most six heads.

$A$ man makes attempts to hit the target. The probability of hitting the target is $\frac{3}{5}$. Then the probability that he hits the target exactly $2$ times in $5$ attempts is:

$A$ 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