$A$ pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

Let $X$ have a binomial distribution $B(n, p)$ such that the sum and the product of the mean and variance of $X$ are $24$ and $128$ respectively. If $P(X > n - 3) = \frac{k}{2^n}$,then $k$ is equal to.

$A$ multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing 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.

When success is not an impossible event,then the mean of Binomial distribution is

$A$ die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.