If a die is thrown $7$ times,what is the probability of getting exactly $5$ four times?

If the standard deviation of the random variable $X$ is $\sqrt{3pq}$ and the mean is $3p$,then $E(X^2) = . . . . . . .$

$A$ pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting a head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$,respectively. Suppose $\alpha$ is the number of heads that appear when $C_1$ is tossed twice,independently,and $\beta$ is the number of heads that appear when $C_2$ is tossed twice,independently. Then,the probability that the roots of the quadratic polynomial $x^2 - \alpha x + \beta$ are real and equal is:

If $X \sim B(9, p)$ is a binomial variate satisfying the equation $P(X=3)=P(X=6)$,then $P(X < 3)=$

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$,then $P(|X-3| < 2)=$