Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that one of them is black and the other is red.

Let $A, B, C$ be three pairwise independent events of a random experiment. If $P(\bar{B} \cup \bar{C}) = \frac{1}{2}$, $P(A) > 0$, $P(B) = b$, and $P(C) = c$, then $P((\bar{B} \cap \bar{C}) \mid A) = $

If three dice are thrown at a time, then the probability of getting the sum of the numbers on them as a prime number is

Let $a, b, c \in \{1, 2, 3, 4\}$. If the probability that $ax^2 + 2\sqrt{2}bx + c > 0$ for all $x \in R$ is $m/n$, where $gcd(m, n) = 1$, then $m + n$ is equal to . . . . . . .

Let $A, B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs is $(1-k)$,the probability that exactly one of $B$ and $C$ occurs is $(1-2k)$,the probability that exactly one of $C$ and $A$ occurs is $(1-k)$ and the probability that all $A, B$ and $C$ occur simultaneously is $k^2$,where $0 < k < 1$. Then the probability that at least one of $A, B$ and $C$ occurs is:

If two numbers $p$ and $q$ are chosen randomly from the set $\{1, 2, 3, 4\}$,one by one,with replacement,then the probability of getting $p^2 > 4q$ is