If the mean and variance of a binomial variable $X$ are $2.4$ and $1.44$ respectively,then the parameters $n$ and $p$ are respectively

If a random variable $X$ follows the Binomial distribution $B(33, p)$ such that $3P(X=0) = P(X=1)$,then the value of $\frac{P(X=15)}{P(X=18)} - \frac{P(X=16)}{P(X=17)}$ is equal to

$A$ random variable $X \sim B(n, p)$ follows a binomial distribution with $n = 6$. If $9P(X = 4) = P(X = 2)$, then the probability of success $p$ is:

If a random variable $X$ follows the Binomial distribution $B(33, p)$ such that $3 P(X=0) = P(X=1)$,then the variance of $X$ 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....................

Consider the following events:
$E_1$: Six fair dice are rolled and at least one die shows six.
$E_2$: Twelve fair dice are rolled and at least two dice show six.
Let $p_1$ be the probability of $E_1$ and $p_2$ be the probability of $E_2$. Which of the following is true?