Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are mutually exclusive?

Let $A = \{1, 3, 5, 7, 9\}$ and $B = \{2, 4, 6, 8\}$. If an ordered pair $(a, b)$ is chosen at random from the Cartesian product $A \times B$,what is the probability that $a + b = 9$?

Two dice are thrown together. The probability that the sum of the two numbers will be a multiple of $4$ is

$A$ die has two faces each with number $1$,three faces each with number $2$,and one face with number $3$. If the die is rolled once,determine $P(1 \text{ or } 3)$.

$A$ number $n$ is chosen at random from $\{1, 2, 3, 4, \ldots, 1000\}$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is: