For a Binomial distribution,$n=6$,if $9 P(X=4)=P(X=2)$,then $q=$

In an examination,there are $10$ true-false type questions. Out of $10$,a student can guess the answer of $4$ questions correctly with probability $\frac{3}{4}$ and the remaining $6$ questions correctly with probability $\frac{1}{4}$. If the probability that the student guesses the answers of exactly $8$ questions correctly out of $10$ is $\frac{27 k}{4^{10}}$,then $k$ is equal to

Five coins,each having faces marked $2$ and $3$,are tossed. The probability of obtaining a total sum of $12$ is:

There are $6$ boxes labelled $B_1, B_2, \ldots, B_6$. In each trial,two fair dice $D_1, D_2$ are thrown. If $D_1$ shows $j$ and $D_2$ shows $k$,then $j$ balls are put into the box $B_k$. After $n$ trials,what is the probability that $B_1$ contains at most one ball?

Let $X \sim B(n, p)$. If $E(X) = 2$ and $Var(X) = 1$, then the probability of getting at most one success is .....

$A$ fair coin is tossed $100$ times. The chance of getting a head an even number of times is