$A$ number $n$ is chosen at random from the natural numbers $2$ to $1001$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person $B$ completes the same work in the same time is $\frac{3}{4}$. If both $A$ and $B$ start doing this work at the same time,then the probability that the work is completed in the given time is

$A$ rational number is selected at random from the distinct rational numbers of the form $p/q$ formed with $p$ and $q$ belonging to the set $\{1, 2, 3, 4, 5, 6\}$. The probability that the rational number selected is a proper fraction is:

From the word $POSSESSIVE$,a letter is chosen at random. The probability of it being $S$ 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 simple?