$A$ fair die is thrown up to $20$ times. The probability that on the $10^{th}$ throw,the fourth six appears is:

How many times must a man toss a fair coin so that the probability of having at least one head is more than $90 \%$?

In a Binomial distribution,$n=4$ and $2 P(X=3)=3 P(X=2)$,then $q=$

The probability of securing a success in a trial is three times that of a failure. The probability of getting at least $4$ successes in $5$ trials is

For an entry to a certain course,a candidate is given $20$ problems to solve. If the probability that the candidate can solve any problem is $\frac{3}{7}$,then the probability that he is unable to solve at most $2$ problems is

In a tournament,a team plays $10$ matches with probabilities of winning and losing each match as $\frac{1}{3}$ and $\frac{2}{3}$ respectively. Let $x$ be the number of matches that the team wins,and $y$ be the number of matches that the team loses. If the probability $P(|x-y| \leq 2)$ is $p$,then $3^9 p$ equals....................