In a binomial distribution $B(n, p = 1/4)$,if the probability of at least one success is $\geq 9/10$,then $n \geq$ ?

If a random variable $X$ follows the binomial distribution with parameters $n=5, p$ and $P(X=2)=9 P(X=3)$,then $p$ is equal to

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

$6$ coins are tossed $320$ times. The probability of getting $5$ heads $2$ times is

$A$ coin is tossed $100$ times. What is the probability of getting a tail an odd number of times?

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