When two dice are rolled,what is the probability that the sum of the numbers on the faces is a multiple of $4$?

$4$-digit numbers are formed using the digits $4, 5, 6, 7, 8, 9$ allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed,then the probability that it is exactly divisible by $3$ is

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
State true or false: (give reason for your answer)
Statement: $A', B', C$ are mutually exclusive and exhaustive.

If a point $A(x, y)$ lies in the region bounded by the $y$-axis,straight lines $2y+x=6$ and $5x-6y=30$,then the probability that $y < 1$ is

$A$ fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is $3$.

$A$ 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: