$A$ die is tossed twice. Getting a number greater than $4$ is considered a success. Then the variance of the probability distribution of the number of successes is

$A$ die is tossed $5$ times. Getting an odd number is considered a success. Then the variance of the distribution of success is

$A$ fair coin is tossed a fixed number of times. If the probability of getting $7$ heads is equal to the probability of getting $9$ heads,then the probability of getting $2$ heads is:

Suppose a machine produces metal parts that contain some defective parts with probability $0.05$. How many parts should be produced in order that the probability of at least one part being defective is at least $1/2$? (Given that, $\log_{10} 95 = 1.977$ and $\log_{10} 2 = 0.3$)

The probability that a man fails to hit a target is $\frac{1}{3}$. If he fires $4$ times,then the probability that he hits the target at least thrice is

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(n_1, 0.5)$ and $Y \sim B(n_2, 0.4)$. If the variance of both $X$ and $Y$ is $6$,then $\sqrt{n_1+n_2}=$