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 $\sqrt{n_1+n_2}=$

The probability of a man hitting a target is $\frac{2}{5}$. He fires at the target $k$ times ($k$ is a given number). The minimum value of $k$ such that the probability of hitting the target at least once is more than $\frac{7}{10}$ is:

Let a die be rolled $n$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{k}{2^{15}}$,then $k$ is equal to:

$A$ multiple choice test consists of $5$ questions,each question having $4$ responses. There is only one correct response and the remaining $3$ are incorrect responses. If a candidate attempts all the $5$ questions,then the probability that he answers at least $3$ questions incorrectly is

$A$ die is thrown four times. The probability of getting a perfect square in at least one throw is

Two cards are drawn successively with replacement from a well-shuffled deck of $52$ cards. Let $X$ denote the random variable of the number of aces obtained in the two drawn cards. Then $P(X = 1) + P(X = 2)$ equals