If two balanced dice are tossed once,the probability of the event that the sum of the integers appearing on the upper faces of the two dice is $9$ is:

Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. Then the probability that $a^2 - b^2$ is divisible by $3$ is (in $/87$)

$A$ person can hit a bird once in three attempts. If the person makes three attempts, what is the probability that the bird is hit (in $/27$)?

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 $\leq 5$.
Describe the events $A$ and $B$.

Let $A$ and $B$ be two independent events of a random experiment. If the probability that both $A$ and $B$ occur is $\frac{1}{6}$ and the probability that neither of them occur is $\frac{1}{3}$,then the probability of occurrence of $A$ is

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment:
$A:$ the sum is even.
$B:$ the sum is a multiple of $3$.
$C:$ the sum is less than $4$.
$D:$ the sum is greater than $11$.
Which pairs of these events are mutually exclusive?