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

The probability that a person wins a prize on a lottery ticket is $\frac{1}{4}$. If he purchases $5$ lottery tickets at random,then the probability that he wins at least one prize is

It is given that the discrete random variable is $X \sim B(n, p)$ and $P(X=2)=P(X=3)$. Find the mean of the distribution.

One out of $9$ ships is likely to sink when they are set on sail. When $6$ ships are set on sail,the probability that exactly $3$ of them will not arrive safely is

In a multiple-choice test consisting of $8$ questions,each question has four options. For each of the questions,exactly one of the four options is the right answer. $A$ student answers all the questions by choosing one option for each question. The number of ways in which the student can get exactly $5$ correct answers 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....................