For a binomial variate $X$ with $n=6$,if $P(X=2)=9 P(X=4)$,then its variance is

When two dice are rolled, let $x$ be the probability that the sum of the numbers appearing on the dice is at most $7$. Let $y$ be the probability of getting a sum of $7$ at least once when a pair of dice are rolled $n$ times. In order to have $y > x$, the minimum value of $n$ is

$A$ 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:

$A$ person fails $4$ times in a game when he plays $9$ times. If he plays $15$ times, the probability of having success at most one is

$A$ die is tossed twice. Getting a number greater than $4$ is considered a success. Then the variance of the probability distribution of the number of successes is

The probability distribution of the number of doublets in four throws of a pair of dice is given by