$A$ pair of $12$-sided fair dice with faces numbered $1, 2, 3, \ldots, 12$ is rolled. The probability that the sum of the numbers appearing has a remainder of $2$ when divided by $9$ is

If four positive integers are selected randomly from the set of positive integers,then the probability that the unit digit of their product is $1, 3, 7,$ or $9$ is:

$A$ pack of cards contains $4$ aces,$4$ kings,$4$ queens,and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace is:

$A$ and $B$ are two candidates seeking admission in a college. The probability that $A$ is selected is $0.7$ and the probability that exactly one of them is selected is $0.6$. Find the probability that $B$ is selected.

$2$ aeroplanes $I$ and $II$ bomb a target in succession. The probabilities of $I$ and $II$ scoring a hit correctly are $0.3$ and $0.2$ respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the $2^{nd}$ plane is

$A$ number $n$ is randomly selected from the set $\{1, 2, 3, \dots, 1000\}$. The probability that $\frac{\sum_{i=1}^n i^2}{\sum_{i=1}^n i}$ is an integer is: