$A$ student writes an examination which contains $8$ true or false questions. If he answers $6$ or more questions correctly,he passes the examination. If the student answers all the questions,then the probability that he fails in the examination is

$A$ fair coin is tossed $K$ times such that the probability of getting $4$ heads is equal to that of getting $6$ heads. If the probability is maximum for getting $r$ heads,then $r=$

How many times must a fair coin be tossed so that the probability of getting at least one head is at least $0.8$?

$A$ and $B$ are playing a chess game with each other. The probability that $A$ wins the game is $0.6$,the probability that he loses is $0.3$,and the probability that it is a draw is $0.1$. If they play three games,what is the probability that $A$ wins at least two games?

In a box containing $100$ bulbs,$10$ are defective. The probability that out of a sample of $5$ bulbs,none is defective 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....................